quantitative evaluation of demineralized and remineralized dental lesions using photothermal

165
QUANTITATIVE EVALUATION OF SIMULATED ENAMEL DEMINERALIZATION AND REMINERALIZATION USING PHOTOTHERMAL RADIOMETRY AND MODULATED LUMINESCENCE by Adam Hellen A thesis submitted in conformity with the requirements for the degree of Master of Science Graduate Department of Dentistry University of Toronto © Copyright by Adam Hellen, 2010

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QUANTITATIVE EVALUATION OF SIMULATED ENAMEL

DEMINERALIZATION AND REMINERALIZATION USING

PHOTOTHERMAL RADIOMETRY AND MODULATED

LUMINESCENCE

by

Adam Hellen

A thesis submitted in conformity with the requirements

for the degree of Master of Science

Graduate Department of Dentistry

University of Toronto

© Copyright by Adam Hellen, 2010

II

Quantitative Evaluation of Simulated Enamel Demineralization

and Remineralization Using Photothermal Radiometry and

Modulated Luminescence

Adam Hellen

Master of Science

Graduate Department of Dentistry

University of Toronto

2010

Abstract

Detection modalities that can evaluate the early stages of dental caries are indispensable. The

purpose of this thesis is to evaluate the efficacy of photothermal radiometry and modulated

luminescence (PTR-LUM) to non-destructively detect and quantify simulated enamel caries.

Two experiments were performed based on the PTR-LUM detection mode: back-propagation or

transmission-mode. Artificial demineralized lesions were created in human molars and a subset

was further exposed to an artificial remineralizing solution. PTR-LUM frequency scans were

performed periodically during de/re-mineralization treatments. PTR data was fitted to a

theoretical model based on optical and thermal fluxes in enamel to extract opto-thermophysical

parameters. Lesion validation was performed using transverse microradiography (TMR). Optical

and thermal properties changed with the development and repair of the caries lesions while

theory-derived thicknesses paralleled those determined microradiographically. These trends

coupled with the uniqueness-of-fit of the generated parameters illustrate the efficacy of PTR-

LUM to non-destructively detect and quantify de/re-mineralized lesions.

III

Acknowledgements

I would like to thank all the lab members at the Center for Advanced Diffusion-Wave

Technologies (CADIFT) and Quantum Dental Technologies (QDT) for their insight and support.

Specifically, I would like to acknowledge Dr. Raymond Jeon, Dr. Anna Matvienko and Dr.

Koneswaran Sivagurunathan for their invaluable assistance, lengthy discussions, suggestions and

guidance over the years. Thank you to Dr. Stephen Abrams for his endless motivation and

clinical insight into the application and development of caries detection aids. His clinical

expertise and knowledge of dental economics are truly invaluable to the dental profession as he

continually tries to promote a shift from the traditional ―drill, fill and bill‖ approach to dentistry.

I would like to express my sincere gratitude toward my supervisors, Dr. Andreas Mandelis and

Dr. Yoav Finer for their endless support, leadership and expertise. Thank you to my advisory

committee member, Dr. Paul Santerre, for his support and discussions. Thank you to Prof.

Mandelis, whose scientific knowledge, perspicacity and motivation made this research project

possible and inspired me to meticulously explore the interminable world of quantitative, non-

destructive science. I would also like to thank Dr. Bennett Amaechi at the University of Texas

Health Science Center at San Antonio for transverse microradiography analysis and his

invaluable discussions relating to the experimental protocol and principles of cariology.

I would like to acknowledge the following funding agencies for financial support: the Ministry of

Research and Innovation (MRI), the Ontario Premier‘s Discovery Award, the Ontario Research

Fund from the Canadian Foundation for Innovation (CFI-ORF) and lastly the Natural Sciences

and Engineering Research Council of Canada (NSERC).

IV

Table of Contents Abstract ........................................................................................................................................... II

Acknowledgements ....................................................................................................................... III

Table of Contents .......................................................................................................................... IV

List of Tables ................................................................................................................................ VI

List of Figures ............................................................................................................................... VI

1 Literature Review................................................................................................................ 1

1.1 Tooth structure ........................................................................................................ 1

1.2 Dental Caries ........................................................................................................... 3

1.3 The demineralization process ................................................................................. 5

1.4 Histopathology of early caries lesions .................................................................... 7

1.5 The remineralization process .................................................................................. 8

1.6 Demineralization and remineralization evaluation techniques ............................. 11

1.6.1 Physical principles underlying light – tooth interactions .......................... 11

1.6.2 Microradiography ...................................................................................... 16

1.6.3 Optical fluorescence techniques ................................................................ 16

1.6.4 Optical Coherence Tomography ............................................................... 19

1.6.5 Photothermal Radiometry and Modulated Luminescence ........................ 20

2 Rationale ........................................................................................................................... 24

3 PTR-LUM Backscatter Mode: Materials and Methods .................................................... 26

3.1 Sample Collection and Sterilization ...................................................................... 26

3.2 Sample Preparation ............................................................................................... 26

3.3 Demineralization and Remineralization Treatments ............................................ 27

3.3.1 Demineralization ....................................................................................... 27

3.3.2 Remineralization ....................................................................................... 28

3.4 PTR-LUM Experimental Setup ............................................................................ 28

3.5 PTR-LUM frequency scans .................................................................................. 30

3.6 Theoretical Model ................................................................................................. 31

3.6.1 Optical Field .............................................................................................. 32

3.6.2 Thermal Wave Field .................................................................................. 36

3.7 Multiparameter Fitting of Experimental Curves ................................................... 37

3.8 Transverse microradiography (TMR) and image analysis.................................... 42

3.9 Statistical analysis ................................................................................................. 43

4 Results ............................................................................................................................... 44

4.1 Sound enamel ........................................................................................................ 44

4.1.1 Microradiographic Analysis and PTR-LUM signals ................................ 44

4.1.2 Theoretical analysis of untreated enamel samples .................................... 45

4.2 Demineralization Group........................................................................................ 46

4.2.1 Microradiographic Analysis and PTR-LUM Signals ................................ 46

4.2.2 Theoretical analysis of demineralized enamel samples ............................ 49

4.3 Remineralization Treatment Groups ..................................................................... 53

V

4.3.1 Microradiographic analysis and visual appearance ................................... 53

4.3.2 Fluoride-free remineralization group ........................................................ 54

4.3.3 Low fluoride (1 ppm) remineralization group........................................... 59

4.3.4 High fluoride (1000 ppm) remineralization group .................................... 63

5 Discussion ......................................................................................................................... 67

5.1 PTR-LUM signals and multiparameter fits of sound enamel ............................... 67

5.2 PTR-LUM signals during short and long-term demineralization ......................... 70

5.2.1 Multiparameter fits of PTR signals during demineralization .................... 71

5.2.2 LUM signal generation during demineralization ...................................... 79

5.3 PTR-LUM signals during short and long-term remineralization .......................... 82

5.4 Errors and Limitations in the extraction of opto-thermophysical properties ........ 89

5.5 Comparison of irradiation wavelengths and future directions .............................. 91

5.6 Summary ............................................................................................................... 92

CHAPTER 2: Transmission mode PTR – LUM........................................................................... 94

6 Rationale ........................................................................................................................... 94

7 Materials and Methods ...................................................................................................... 95

7.1 Sample Preparation ............................................................................................... 95

7.2 PTR-LUM frequency scans .................................................................................. 96

7.3 Demineralization and Remineralization Treatments ............................................ 97

7.4 PTR-LUM Experimental Setup ............................................................................ 97

7.5 Transverse microradiography (TMR) and image analysis.................................... 98

8 Results ............................................................................................................................... 98

8.1 Time-series demineralization experiments ........................................................... 98

8.2 Time-series remineralization experiments .......................................................... 100

9 Discussion ....................................................................................................................... 102

9.1 PTR-LUM signals and time-series demineralization .......................................... 102

9.2 PTR-LUM signals and time-series remineralization .......................................... 106

9.3 Errors and limitations of transmission PTR-LUM measurements ...................... 107

9.4 Future directions ................................................................................................. 108

10 Significance..................................................................................................................... 109

11 Summary ......................................................................................................................... 113

12 Conclusions ..................................................................................................................... 113

13 Appendices ...................................................................................................................... 115

13.1 Appendix 1 .......................................................................................................... 115

13.2 Appendix 2 .......................................................................................................... 119

13.3 Appendix 3 .......................................................................................................... 123

13.4 Appendix 4 .......................................................................................................... 128

13.5 Appendix 5 .......................................................................................................... 131

14 References ....................................................................................................................... 136

VI

List of Tables

Chapter 1

Table 1. Published optical properties of sound and carious enamel at relevant wavelengths. ..... 14

Table 2. Published set of thermal properties of sound and carious enamel. ................................. 15

Table 3. Laser parameters for backscatter PTR-LUM measurements. ......................................... 29

Table 4. Treatment groups for backscatter PTR-LUM ................................................................. 27

Table 5. Composition of the remineralizing solution. .................................................................. 28

Table 6. The list of parameters fitted from the theoretical analysis. ............................................. 32

Table 7. Fixed upper and lower limits of the fundamental parameters defined for the

multiparameter fitting of untreated enamel. .......................................................................... 40

Table 8. Mean (± s.d.) set of derived optical and thermal parameters of intact enamel layers .... 46

Table 9. General trends in the main physical parameters following short and long term

demineralization.. .................................................................................................................. 53

Table 10. Average mineral loss and lesion depth of remineralization and demineralized treatment

groups.. .................................................................................................................................. 54

Table 11. General trends in the main physical parameters following demineralization and short

vs. long term remineralization. .............................................................................................. 67

Chapter 2

Table 2.1. Treatment groups for transmission-mode PTR-LUM study. ....................................... 97

List of Figures

Chapter 1

Figure 1. A human molar in situ showing the primary tissue components and surrounding tooth

structures. ................................................................................................................................. 1

Figure 2. A scanning electron microscopic view of (A) the three primary tissues of teeth, and the

spatial organization of enamel and relationship between rods (R) and inter-rod (IR) spaces

viewed longitudinally (B) or in cross section (C). (D) Mature, permanent, human enamel

showing superficial aprismatic enamel overlying prismatic enamel... .................................... 2

Figure 3. The dynamic demineralization-remineralization equilibrium at the plaque-enamel

interface. Saliva acts as a source of mineral and fluoride ions promoting lesion

remineralization. ...................................................................................................................... 4

Figure 4. The pH dependence on enamel caries formation and remineralization. ......................... 5

VII

Figure 5. (A) Classical enamel caries lesion with surface layer and demineralized lesion body

clearly evident under polarized light microscopy. A clear distinction of carious zones is

evident in the image (A) and microdensitometric profile of the lesion (B). The mineral

volume percent is plotted vs. depth (d) from the surface. ....................................................... 8

Figure 6. Light- tissue interaction. ................................................................................................ 12

Figure 7. Wavelength dependence of (A) the water absorption coefficient and (B) the infrared

transmission properties of the primary absorbers in dental enamel. ..................................... 13

Figure 8. Photothermal and luminescence effects upon excitation with an intensity modulated

laser beam. ............................................................................................................................. 22

Figure 9. Experimental setup for backscatter-mode PTR-LUM study ......................................... 30

Figure 10. The 3-layer geometrical representation used for theoretical analysis and associated

optical and thermal parameters of each layer. ....................................................................... 33

Figure 11. Schematic geometry of effective layers for multiparameter fittings of sound enamel.38

Figure 12. Schematic structure of effective layers used for fits of demineralized and

remineralized enamel. ............................................................................................................ 40

Figure 13. Schematic mineral content profile for the theoretical determination of layer

thicknesses. ............................................................................................................................ 41

Figure 14. Visual appearance of (a) sound enamel and (b) white-spot appearance after 10-days of

acid treatment. ....................................................................................................................... 44

Figure 15. PTR-LUM amplitudes and phase curves for a representative sound enamel sample

under 660-nm laser excitation. The densitometric tracing (top right) and microradiographic

image (bottom right) are presented in the adjacent figures.. ................................................. 45

Figure 16. PTR-LUM amplitudes and phase curves for a 10 day demineralized sample under

660nm laser excitation. Error bars, when not visible, are of the size of the symbols. The

densitometric tracing (top right) and microradiographic image (bottom right) of the lesion

are presented in the adjacent figures. ..................................................................................... 48

Figure 17. PTR-LUM signals for the 40 day demineralized lesion under 660-nm. Error bars,

when not visible, are of the size of the symbols. The densitometric tracing (top right) and

microradiographic image (bottom right) of the lesion are presented in the adjacent figures. 49

Figure 18. The change in optical absorption (a) and scattering (b) coefficients and thermal

conductivity (c) and diffusivity (d) parameters as a function of time, over the 10 day

demineralization period.. ....................................................................................................... 50

VIII

Figure 19. Changes in the thickness of layer 1 and layer 2 as a function of time for the 10 day (a)

and 40 day (b) demineralized samples. The inset in (b) shows the details of layer 1 thickness

over time on an expanded scale.. ........................................................................................... 51

Figure 20. The change in optical absorption (a) and scattering (b) coefficients and thermal

conductivity (c) and diffusivity (d) parameters as a function of time over the 40 day

demineralization period.. ....................................................................................................... 52

Figure 21. Visual appearance of representative samples from each remineralization treatment

group. (a) Remineralized in the absence of fluoride; (b) remineralized in the presence of low

fluoride; (c) remineralized in the presence of high fluoride levels. ....................................... 53

Figure 22. Microradiographic image and mineral volume profile for an exemplary sample from

the fluoride-free treatment group. .......................................................................................... 55

Figure 23. PTR-LUM amplitude ratios and phases differences with respect to the final

demineralization state for a sample in the fluoride-free treatment group, under 660nm laser

excitation.. ............................................................................................................................. 56

Figure 24. Change in optical absorption (A) and scattering coefficients (B) over treatment time

for a sample in the fluoride-free treatment group.. ................................................................ 57

Figure 25. Change in thermal conductivity (A) and diffusivity (B) over treatment time for a

sample in the fluoride-free treatment group.. ........................................................................ 58

Figure 26. Change in layer thicknesses over treatment time for a sample in the fluoride-free

treatment group. ..................................................................................................................... 58

Figure 27. Microradiographic image and mineral volume profile for an exemplary sample from

the low fluoride treatment group. .......................................................................................... 59

Figure 28. PTR-LUM amplitude ratios and phases differences with respect to the final

demineralization state for a sample in the low fluoride treatment group, under 660nm laser

excitation. .............................................................................................................................. 60

Figure 29. Change in optical absorption (A) and scattering coefficients (B) over treatment time

for a sample in the low fluoride treatment group.. ................................................................ 61

Figure 30. Change in thermal conductivity (A) and diffusivity (B) over treatment time for the

low fluoride sample. ..................................................................................................................

............................................................................................................................................... 62

Figure 31. Change in layer thicknesses over treatment time for a sample in the low fluoride

treatment group. ..................................................................................................................... 62

Figure 32. Microradiographic image and mineral volume profile for an exemplary sample from

the high fluoride treatment group. ......................................................................................... 63

IX

Figure 33. PTR-LUM amplitude ratios and phase differences with respect to the final

demineralization state for a sample in the high fluoride treatment group, under 660nm laser

excitation.. ............................................................................................................................. 64

Figure 34. Change in optical absorption (A) and scattering coefficients (B) over treatment time

for a sample in the high fluoride treatment group.. ............................................................... 65

Figure 35. Change in thermal conductivity (A) and diffusivity (B) over treatment time for a

sample in the high fluoride treatment group. ......................................................................... 66

Figure 36. Change in layer thicknesses over treatment time for a sample in the high fluoride

treatment group. ..................................................................................................................... 66

Chapter 2

Figure 2.1. Experimental apparatus for transmission experiments. .............................................. 96

Figure 2.2. Experimental setup for transmission-mode PTR-LUM. ............................................ 98

Figure 2.3. Exemplary microradiograph (a), densitometric tracing (b), and visible light

transmission image (c) of a demineralized enamel section. .................................................. 99

Figure 2.4. Time-series transmission-mode PTR-LUM amplitude and phase signals at 1Hz (PTR)

and 89Hz (LUM) for a sample demineralized for 15 days. ................................................... 99

Figure 2.5. Time-series transmission PTR-LUM amplitude and phase signals at 1Hz (PTR) and

89Hz (LUM). Vertical dashed lines divide de-and remineralization treatments. The visible

light transmission image (top right) and microradiographic image (bottom right) are

presented in the adjacent figures. ........................................................................................ 101

Figure 2.6. Microradiograph and mineral content profile of a de- and remineralized sample. The

corresponding PTR-LUM signals are presented in Fig. 2.7.. .............................................. 101

Figure 2.7. Time-series transmission PTR signals at 1 Hz (A) and transmission LUM at 89Hz

(B). (C) Time-series LUM signals at 89 Hz viewed in backscatter mode.. ......................... 102

1

1 Literature Review

1.1 Tooth structure

Human teeth are composed of three primary tissues and moving from the surface exposed to the

oral environment inward they are: enamel, dentin, and pulp (Fig. 1). Enamel is the outer

mineralized tissue exposed to the oral environment, forming a protective layer at the anatomical

crown of the teeth. Dentin occupies the largest portion of the overall tooth structure and encloses

the pulp chamber.

Figure 1. A human molar in situ showing the primary tooth tissue components and surrounding

tooth structures [Adapted from Nanci 2003].

Enamel is the complex, non-vital, secretory product of specialized epithelial cells called

ameloblasts. The process of enamel formation can be broadly categorized into two stages. The

first stage, called the secretory stage, involves the organized secretion of a protein-rich and

acellular matrix, packed with thin, ribbon-like crystals of hydroxyapatite (OHAp) into prisms (or

rods) (Smith 1998). The second stage, referred to as the maturation stage, involves the growth of

crystals at the expense of protein and enamel fluid, which are absent in mature enamel (ten Cate

1998). In mature enamel, OHAp crystals are approximately 30 – 40 nm in diameter and can be

up to 10 µm long. The OHAp crystals pack together forming the enamel prisms, which typically

have an overall cross-section of 4 – 6 µm (Fig. 2). The end result of enamel formation is the

creation of an acellular tissue which is composed of approximately 95 wt% (≈85 vol%) of an

impure mineral OHAp with the remainder made up of non-collagenous protein and water

2

(Dowker et al. 1999; Featherstone 2000). The spaces created at the interface between prisms is

occupied by ≈12 % by volume water and ≈3 % by volume organic material, thus creating about

≈15 % by volume of available diffusible space for acids and inorganic mineral ions (Kidd and

Joyston-Bechal 1997; Featherstone 1999)(Fig. 2).

Figure 2. A scanning electron microscopic view of (A) the three primary tissues of teeth, and the

spatial organization of enamel and relationship between rods (R) and inter-rod (IR) spaces

viewed longitudinally (B) or in cross section (C) [Adapted from Nanci 2003]. (D) Mature,

permanent, human enamel showing superficial aprismatic enamel overlying prismatic enamel.

ES = enamel surface. Bar = 50 µm. [Adapted from Kodaka et al. 1991].

At the outermost surface of enamel, a region of aprismatic enamel has been described distinct

from underlying prismatic structure (Gwinnett 1967; Kodaka 2003) (Fig. 2D). The term

―aprismatic‖ does not imply the layer is altogether structure-less, but rather refers to the absence

of characteristic prism markings with the parallel arrangement of needle-shaped crystallites. The

aprismatic enamel layer is most likely formed as a result of the reduced functional activity of

ameloblasts during the terminal stages of amelogenesis (Ripa et al. 1966). It is prevalent in both

unerupted and erupted permanent and deciduous dentition, although more likely to be observed

in unerupted and deciduous teeth, with a range of thicknesses from a few microns to

approximately 60 µm in erupted teeth (Kakaboura et al. 2005). It is present in about 70% of

permanent erupted human molars, with its prevalence most likely linked to its wear over time as

a result of abrasive and masticatory forces and post-eruptive maturation processes (Gwinnett

1967; Ripa et al. 1966). As permeability and caries susceptibility of newly erupted enamel is

very high, the natural post-eruptive maturation process occurs to create a more stable and less

soluble enamel surface through the precipitation of fluoridated-OHAp phases.

The impure nature of enamel mineral is reflected in its propensity to accommodate numerous

ionic substitutions and vacancies within its crystal lattice without losing its apatitic structure

A B C D

3

(Aoba 2004). Extraneous ions most commonly found within the enamel apatite include cations,

magnesium and sodium and anions, carbonate and fluoride (Robinson et al. 2000). As a

consequence of these impurity atoms, defects are introduced within the OHAp crystal lattice

thereby altering the solubility product of the mineral (ten Cate and Featherstone 1991).

Composition of the impurity elements varies with depth, with higher carbonate and magnesium

concentrations in areas of lower crystallinity closer to the dentin-enamel junction (DEJ) and

higher fluoride levels at the enamel surface (Weatherell et al. 1974).

As enamel is highly mineralized and brittle, in order to avoid fracture under regular masticatory

forces it requires additional support, which is provided by the more resilient dentin (Nanci 2003).

In contrast to enamel, it is a vital tissue made up of closely-packed micrometer-sized cylinders

with a higher mineralized shell, called dentinal tubules, which contain dentinal fluid and the

cytoplasmic extensions of the odontoblasts, the dentin-forming cells. Dentin, as in bone, is

formed with OHAp crystals organized about an abundant organic matrix. It is composed of about

47 vol.% carbonated-rich and calcium deficient OHAp mineral, about 33 vol.% organic material,

mainly Type-I collagen, and the remaining ≈20 vol.% water (Marshall et al. 1997; Curzon and

Featherstone 1983). The lower crystallinity and higher organic component of dentin makes it a

porous and more acid soluble tissue. The pulp chamber, enclosed by the dentin, contains soft

connective tissue and is innervated by nerves. It serves several functions including the formation

of dentin, provides nutrients to avascular dentin and can repair dentin when required (Nanci

2003).

1.2 Dental Caries

Dental caries is an infectious, ubiquitous and multifactorial disease affecting nearly all mankind.

The chronic, slowly progressing caries process involves the localized destruction of dental hard

tissue, initially in enamel followed by dentin, as a result of acids produced from bacterial

fermentation of dietary carbohydrates by the cariogenic microflora of dental plaque (Selwitz et

al. 2007). Caries encompasses a continuum of disease states where an intimate balance between

demineralization and remineralization can be found sub-clinically localized initially to the outer

enamel, progressed into dentin or advanced in root tissue (Fig. 3).

4

Figure 3. The dynamic demineralization-remineralization equilibrium at the plaque-enamel

interface. Saliva acts as a source of mineral and fluoride ions promoting lesion remineralization

[Adapted from Winston and Bhaskar 1998].

Demineralization refers to the process by which bacterially-derived plaque acids generated under

mildly acidic conditions diffuse into the tooth mineral structure (Fig. 2), causing destruction of

enamel and/or dentin crystals. As enamel destruction continues and the lesion progresses into the

underlying dentin, bacterial invasion will occur with the concomitant diffusion of acids. As a

result, death of the pulp and spread of infection to periapical tissues may occur (Kidd and

Joyston-Bechal 1997). Under strongly acidic conditions, such as those generated by gastric acids

and acidic beverages, an erosive challenge can result in the often irreversible loss of tooth

structure (Fig. 4). The repair process, remineralization, occurs under near-neutral physiological

pH conditions whereby calcium and phosphate mineral ions are re-deposited within the caries

lesion from saliva and plaque fluid (Fig. 3). Although the processes of demineralization and

remineralization are described separately, it is their intimate balance, modulated by host factors

such as diet, salivary flow and composition, carbohydrate frequency and duration and the

maintenance of oral hygiene, that ultimately determines an individual‘s overall caries risk

(Selwitz et al. 2007; Aoba 2004). As a result, over time, early lesions left uncared for may

cavitate, while if diagnosis at the incipient stage timely therapies can be instituted to repair the

lesions to restore form and functionality.

5

Figure 4. The pH dependence on enamel caries formation and remineralization (Adapted from

Pretty 2006, modified from Mount and Hume 2005).

1.3 The demineralization process

Demineralization refers to the destruction of OHAp by organic acids (predominately lactic acid)

in their unionized form, generating a concentration gradient for the dissolution of calcium and

phosphate and diffusion from the bulk tissue (Featherstone et al. 1979) (Fig. 3). The process of

demineralization involves active mineral loss at the advancing front of the lesion, at a depth

below the enamel surface, with the transport of acid ions from the plaque to the advancing front

and mineral ions from the advancing front toward the plaque. Thus over time, the advancing

lesion front moves deeper into the enamel at the expense of underlying sound enamel, while an

intact surface layer above the lesion modulates the reaction between the internal demineralizing

structure and external solution (Fig. 5). During the initial caries attack, direct surface enamel

dissolution causes an enlargement of the intercrystalline spaces over the enamel surface thereby

facilitating the movement of acids and mineral ions into and out of the porous enamel structure.

This may indicate preferential loss of more acid-soluble phases of enamel mineral, carbonate and

magnesium-rich phases, as well as facilitated diffusion of acids through the enamel

microstructure due to lower crystal density at these particular sites (Robinson et al. 2000).

Thermodynamically, appropriate physicochemical conditions at the tooth-solution interface are

needed in order to favour either demineralization or remineralization. These conditions refer to

the saturation level of the solution in direct contact with enamel. The pH at which the solution in

direct contact with the tooth is saturated with respect to enamel mineral is referred to as the

‗critical pH‘ value and is typically around 5.5 (Dawes 2003). Below the critical pH value

dissolution will be favoured, whereas above mineral precipitation reactions are favoured (Fig. 4).

The rate at which mineral is lost from enamel and the depth to which the lesion progresses is a

HA is hydroxyapatite FA is fluorapatite

6

function of the rate-limiting process. Historically, the dissolution process in enamel was

described by a diffusion-control mechanism, where the rate-determining step was the transport of

mineral ions to-and-from the dissolution site at the advancing front of the lesion (Gray 1962;

Featherstone et al. 1979; Christoffersen and Arends 1982; Poole et al. 1981). More recent

evidence has suggested a surface-controlled mechanism of enamel demineralization, where the

rate of reaction was determined by the crystalline-level chemical dissolution processes at the

advancing front of the developing lesion (Josselin de Jong et al. 1987; Margolis and Moreno

1992; Gao et al. 1993b; Margolis et al. 1999; Anderson et al. 1998). It is likely however, that

dissolution processes in vitro and in vivo, entail a continuum of surface and diffusion controlled

mechanisms (Elliott et al. 2008), as enamel porosity, the presence of dissolution inhibitors from

saliva, mineral solubility and exposed surface area for dissolution may all influence the

governing reaction control mechanism (Anderson et al. 1998).

In order to gain insight into de- and remineralization mechanisms in a more controlled state,

artificial demineralizing systems have been developed to reproducibly create carious lesions

indistinguishable from natural caries lesions. A requirement for chemical demineralizing systems

is the incorporation of a surface inhibitor, partial saturation conditions and/or the modification of

the viscosity of the demineralizing medium. Surface inhibitors have taken form as one or a

combination of the following: incorporation of fluoride ions, diphosphonates, polyacrylic acid or

hydroxyethyl cellulose/carboxymethyl cellulose. The observation that an essentially intact outer

layer is maintained or forms superficial to a demineralized lesion body is remarkable. Over the

years, several theories have been proposed as to explain the origin of this layer. Inhibitors of

surface dissolution have been implicated in surface layer formation by adsorbing to enamel

surfaces rendering it less soluble and as a result acid must diffuse to deeper depth to find more

soluble mineral phases. Surface layer formation has also been related to the intrinsic structural

and chemical gradients in enamel, which significantly impact thermodynamic solubilities.

However, as early studies demonstrated that subsurface lesions could be created in OHAp pellets

and other permeable solids in the absence of surface inhibitors, fluoride, or chemical and

structural gradients, these influences alone could not be responsible for subsurface lesion

formation in enamel and other mechanisms were sought to explain surface layer formation (Aoba

et al. 1978; Anderson and Elliott 1985). These include the kinetic and thermodynamic model

7

based on the calcium phosphate solubility diagrams (Margolis and Moreno 1985), the coupled-

diffusion mechanism, where the chemical potential of one component influences the diffusion

properties of another (Anderson and Elliott 1987; Anderson et al. 2004) and gradients and

transport processes occurring during the dissolution process, where the out-diffusion of mineral

ions from subsurface layers to the bulk solution will reprecipitate within the surface zone

(Moreno and Zahradnik 1974). In summary, it is likely that the aforementioned mechanisms

operate in concert in order to produce subsurface demineralized lesion in enamel. The selection

of an appropriate demineralizing agent is critical in studies investigating efficacies of

remineralizing agents. It is important to note that parameters of a developed artificial lesion, such

as mineral loss, lesion depth and the mineral content of the surface layer, have a marked impact

on the outcome of subsequent remineralization (Lynch et al. 2007).

1.4 Histopathology of early caries lesions

The earliest macroscopic clinical evidence of caries in enamel is the presence of a ‗white-spot

lesion‘. The chalky-white discoloration of a white spot lesion as compared to sound enamel is the

result of a site-specific increase in porosity, which alters the light scattering properties of enamel

(Kidd and Joyston-Bechal 1997). White spot lesions are characterized by subsurface

demineralization below an apparently intact, mineralized surface layer (Fig. 5). The histological

appearance of a white spot lesion manifests itself as a crude 3-layered geometrical profile (Fig.

5). This profile consists of a relatively intact and unaffected surface layer at the most superficial

aspect of the lesion and overlying a demineralized lesion body, which makes up the largest

portion of a carious lesion, where bulk mineral loss occurs. Deep to the demineralized lesion

body is the presence of unaffected, sound enamel. The surface zone is essential in controlling the

rate and extent of both demineralization and remineralization processes and its destruction and

collapse will lead to cavitation (Robinson et al. 2000; Kidd and Joyston-Bechal 1997).

8

Figure 5. (A) Classical enamel caries lesion with surface layer and demineralized lesion body

clearly evident under polarized light microscopy (Adapted from Featherstone 2008). A clear

distinction of carious zones is evident in the image (A) and microdensitometric profile of the

lesion (B). The mineral volume percent is plotted vs. depth (d) from the surface. dsl denotes the

approximate thickness of the surface layer (SL) covering the lesion body (L); df refers to the

position of the lesion front (adapted from Arends and Christoffersen 1986).

1.5 The remineralization process

At neutral pH without acid challenge, the main driving force for remineralization is the passive

transport of salivary or plaque calcium and phosphate ions down their concentration gradient into

the lesion body (Chow and Vogel 2001) (Fig. 3). Soluble calcium phosphate phases are

transformed to a solid and less acid soluble phase through the precipitation of fluorapatite (FAP)

or fluoridated hydroxyapatite (F-OHAp) on existing demineralized crystallites or through the

nucleation of new crystallites. This remineralization process is a natural chemically inorganic

process that does not require soft-tissue or cellular biological processes (Featherstone 2009), as

in bone and dentin remodelling mechanisms. As the remineralization process in vivo takes

considerable amount of time, a multitude of studies have investigated ways to enhance this

process, the most well-documented being fluoride incorporation. Fluoride has been known for

decades to inhibit lesion demineralization and promote consolidation by crystal growth as

fluoride enhances the driving force for mineral precipitation (ten Cate and Featherstone 1991).

Due to its anionic character, fluoride has a high affinity for positive ions such as calcium (CDC

2001). Fluoride ions can substitute completely, or partially, for the OH- ions in the OHAp lattice

to give rise to the formation of the mineral FAP or F-OHAp, respectively. The displacement of

OH- ions with F

- ions in the OHAp lattice results in increased stability, and reduction in the

volume of the unit cell, creating a less soluble apatitic phase (Aoba 1997). Plaque contains a

large amount of fluoride in many different forms, free, loose, bound or firmly bound and each

(A) (B)

9

affect relative de- and remineralization processes in different ways (ten Cate 1983). In its tooth-

bound state, fluoride incorporated during enamel maturation is stable and does not play a

significant role in the remineralization process, whereas ambient free fluoride levels have been

implicated as the major determinants in promoting remineralization of enamel lesions (Faller

1995; Chow and Vogel 2001; Wong et al. 1987). As a result, the post-eruptive effect of a

topically applied fluoride, through varnishes, dentifrices or mouthwashes, is essential in

modulating the dynamic equilibrium at the tooth‘s surface promoting remineralization of

demineralized lesions (Fejerskov et al. 1994, Aoba 1997).

The mechanism of fluoride incorporation as FAP concomitant with its strong affinity for calcium

ions has been the basis for numerous in vivo and in vitro studies demonstrating enhanced

remineralization, particularly in the presence of low fluoride concentrations in solution

(Featherstone and Zero 1992; ten Cate 1990; ten Cate 1997). Varughese and Moreno (1981)

found an increase in the rate of crystal growth when fluoride was added to a calcifying solution

at concentrations as low as 0.05 ppm. Silverstone et al. (1981) found a substantial reduction

(72%) in lesion area when fluoride at 1 ppm was added to a calcifying solution compared to the

same solution in the absence of fluoride (22%). In the same study and in others, no additional

effect was observed in solutions containing 10 ppm fluoride, illustrating that only low levels of

fluoride are required to induce remineralization throughout the body of the lesions (Zahradnik

1979; Silverstone et al. 1981). A similar significant uptake of mineral was observed in other

studies implementing a 1 ppm fluoride solution (ten Cate and Arends 1977; Zahradnik 1979;

Koulourides et al. 1974; ten Cate 2001; Thuy et al. 2008; Nancollas 1979; Lammers et al. 1991;

Amjad and Nancollas 1979; Iijima et al. 1999; Zimmerman et al. 1978). Crystal diameters that

decreased substantially within the demineralized zones were found to increase significantly in

size following remineralization toward the sound enamel level and in some cases produced

diameters 2 - 3x the size of sound enamel crystals (Silverstone 1977; Silverstone et al. 1981;

Silverstone 1983; ten Cate and Arends 1977; Arends and Jongebloed 1979). Employing high

fluoride concentrations, at the levels contained in mouthrinses, varnishes and dentifrices, calcium

fluoride (CaF2) or a calcium-fluoride-like material is formed, and has been suggested to act as a

pH-dependent fluoride reservoir which would release fluoride under subsequent acidic

challenges (ten Cate 1997).

10

Although intuitively mineral reintroduction into porous demineralized enamel from saliva seems

simple, this process does not proceed without its challenges. One challenge relates to the

limitation of remineralization by the diffusion of ions from the external solution (ten Cate 1990).

With excessive fluoride concentrations and/or large enamel supersaturation conditions rapid

mineral deposition may occur preferentially within the enamel surface layer and obstruct surface

enamel porosities leading to a disconnect between the external environment (saliva and plaque

fluid) and the internal environment (subsurface lesion body). Thus, the deposition of mineral at a

particular depth within a caries lesion depends on both the local availability of partially

demineralized crystallites, which act as mineral scaffolds, as well as the local supersaturation,

fluoride levels and pH (ten Cate 1990). The aforementioned mechanism of enhanced surface

layer mineral deposition has been proposed to explain the fact that remineralization is never

complete (Larsen and Fejerskov 1989; Pearce et al. 1995; Chow and Vogel 2001; Arends and ten

Cate 1981; Lagerweij and ten Cate 2006) and points to the accelerated effects of fluoride-

induced remineralization during the initial stages whereas a plateau effect is often observed at

later periods (Al-Khateeb et al. 2000). However, additional factors such as the presence of

salivary proteins in vivo also play a vital role (Zahradnik 1979; Fujikawa et al. 2008). A clinical

lesion judged as not progressing (or inactive) and where surface enamel is restored chemically

and mechanically above a subsurface lesion is termed an arrested lesion. In contrast to active

lesions, arrested lesions are inherently stable and do not respond to remineralization therapies.

Thus, the clinical activity of a lesion is vital in determining susceptibility to remineralization

therapies and preventing overtreatment of lesions that are chemically stable.

An unfavourable trade-off of fluoride ingestion to reduce caries is dental fluorosis. This results

from excessive intake of fluoride during enamel development (Aoba and Fejerskov 2002).

Fluorotic enamel appears histologically as hypomineralization of the subsurface enamel, covered

by a well-mineralized outer surface layer (Fejerskov et al. 1994). The severity of dental fluorosis

is due to the cumulative effect of fluoride over time and therefore can act as a direct indication of

the degree of past fluoride exposure. However, even low levels of fluoride ingestion

(approximately 0.03 mg/kg body weight) can result in weak fluorotic manifestations in the

enamel (Aoba and Fejerskov 2002). More severe cases of dental fluorosis are characterized by

extensive hypomineralization of the porous subsurface layer with exceptionally brittle

11

mineralized surface enamel that may be susceptible to the formation of defects under regular

forces during mastication (Fejerskov et al. 1994). Moderate-to-severe fluorosis is observed as

pits and grooves on the enamel surface or a mottled appearance (Limeback 1994).

1.6 Demineralization and remineralization evaluation techniques

1.6.1 Physical principles underlying light – tooth interactions

When light interacts with teeth, a fraction is reflected, scattered or transmitted from the tissue

and a part may be absorbed within the tissue (Fig. 6). The absorbed energy can be converted

non-radiatively or radiatively as heat or fluorescence, respectively. Scattering refers to the

process whereby a photon changes its path without losing its energy. This typically occurs

following the interaction of photons with small particles or inhomogeneities within the tissue

volume. Following absorption events, further scattering or transmission events can take place.

Fundamental processes underlying light-tissue interactions involve optical phenomena within the

tissue volume. Parameters used to characterize tissue optical properties include, photon

scattering (μs) and absorption coefficients (μa), which refer to the average number of absorption

and scattering events per unit length of a photon propagating though the medium (Minet et al.

2006). Together they amount to the total attenuation coefficient, given as: μt = μa + μs and is an

important optical parameter defining the total optical penetration depth in a tissue at a given

excitation wavelength (Minet et al. 2006). As noted earlier, enamel and dentin are composite

materials with chemical and structural gradients varying as a function of depth. As a result, light

propagation in enamel and dentin, as in other biological media, can be described as a highly

scattering random medium, i.e. turbid tissue. Scattering in tissues is a result of structural

inhomogeneities and a function of the wavelength of light. There is a direct relationship between

scattering and the wavelength of light, where longer wavelengths scatter less than shorter

wavelengths and consequently offer deeper penetration into tissues. However, deeper penetration

comes at the expense of a poorer resolution (Hall and Girkin 2004). In addition to μs, the

scattering phase function (g), also referred to as the anisotropy factor or cosine of the scattering

angle, describes the directional nature of scattering events and is highly dependent on the nature

of the scattering medium. Biological tissues are highly forward scattering (g ≈ 1) in the visible,

meaning light paths are long with high absorption probabilities, with typical g values between

12

0.79 - 0.98 (Cheong et al. 1990). By measuring the aforementioned optical constants, light

transport process within a tissue, such as tooth enamel, can be almost completely described.

Figure 6. Light- tissue interaction. See text for description. [Adapted from Hall and Girkin

2004].

For the detection of early caries the selection of the correct wavelength of light is vital. The

wavelength must be chosen such that sound enamel is transparent, meaning light absorption is

minimal. This typically occurs at the longer wavelength end of the visible spectrum (visibly red)

and into the infrared, as light scattering and absorption processes are much lower and therefore

transmission is optimal (Featherstone and Fried 2001). However, farther into the infrared

absorption coefficients markedly increase due to the strong absorption peak of water (Fig. 7A,

B). Wavelengths in the range ≈2 µm < λ > ≈650-nm ensure optimal light penetration within

biological tissues (Gupta et al. 2007).

13

Figure 7. Wavelength dependence of (A) the water absorption coefficient (Modified from Gupta

et al. 2007) and (B) the infrared transmission properties of the primary absorbers in dental

enamel (Modified from Featherstone and Fried 2001).

The presence of defects in enamel (caries lesion) will alter optical scattering and absorption

properties which subsequently influence converted energy signals, such as thermal emissions or

fluorescence intensity (Hall and Girkin 2004). A detailed list of optical absorption and scattering

coefficients for sound and carious enamel are presented in Table 1. These optical properties play

a vital role in determining the energy distribution within the tissue volume. Larger values for

these coefficients indicate that incident photons are absorbed rapidly in near-surface regions,

resulting in smaller penetration depths and poorer resolution of deeper underlying structures. The

origin of light scattering in enamel has been ascribed to both the crystallites and prisms

components of enamel. Typical absorption and scattering properties for dentin, not included

within Table 1, are much larger than the corresponding values for enamel. A larger absorption

coefficient of approximately 300 – 400 m-1

is typical of dentin and may be related to the larger

organic makeup of dentin compared to enamel. Although not considered in the present

investigations, the scattering properties of dentin were found to be highly dependent on the

density of tubules rather than mineral content and varied from 3000 – 20 000 cm-1

over the

visible light spectral range (400 – 700 nm) (Zijp and ten Bosch 1991).

Teeth, similar to other biological tissues, are complex multi-layered structures with absorption

and scattering properties changing as a function of depth. As a result, attempts to derive

complete analytical solutions to model light propagation within the tissue volume are both

impractical and virtually impossible. Rather approximations are implemented. Historically,

(A) (B)

14

optical properties of enamel and dentin have been determined by measurements of the

reflectance and transmission through thin sections followed by the application of a theoretical

formalism to the experimental data to extract optical absorption and scattering coefficients.

Theoretical models typically used include Kubelka-Munk theory (Ko et al. 2000; Zijp 2001) or

the Monte Carlo approach (Fried et al. 1993; Fried et al. 1995; Mujat et al. 2003). The

determination of the aforementioned optical parameters (μa, μs and g) is a difficult task requiring

the use of complex numerical models, assumptions and approximations which explains why

there have been relatively few reports on optical evaluation of dental tissues. Furthermore, the

use of thin sections, mostly of known thickness, is a requirement for transmission measurements.

These preparative samples add additional variability that does not reflect the conditions in the

oral cavity, thus making it difficult to relate in vitro determined optical properties of prepared

sections to intact substrates in vivo (Chebotareva et al. 1993).

Table 1. Published set of optical properties of sound and carious enamel at relevant wavelengths.

* Bovine enamel sections

ffi Zijp (2001), calculated from Spitzer and ten Bosch (1975)

† From diffuse reflectance and transmittance by a modified CCD camera method

Optical Properties of Enamel

Wavelength (nm)

Absorption coefficient μa, [m

-1] Scattering coefficient

μs, [m-1]

References

Sound Enamel

543 <100 10 500 Fried et al. (1995)

600 7 000* Groenhuis et al. (1981)

600 3 300 Groenhuis et al. (1981)

600 <100 ≈6400 Mobley and Vo-Dinh (2003)

632 <100 6 000 ± 1 800 Fried et al. (1995)

632 97‡ 2 300‡ Spitzer and Ten Bosch (1975)

633 6 600 Zijp et al. (1995)

633 97 110 Zijp (2001) and references therein

633 40 1 000‡ Spitzer and Ten Bosch (1975)

700 <100 ≈5000 Mobley and Vo-Dinh (2003)

700 5 500* Groenhuis et al. (1981)

700 2 700 Groenhuis et al. (1981)

800 <100 ≈3300 Mobley and Vo-Dinh (2003)

1000 <100 ≈1600 Mobley and Vo-Dinh (2003)

1053 <100 1 500 Fried et al. (1995)

1 730 – 5 140†* Ko et al. (2000)

Carious Enamel

600 55 000 Groenhuis et al. (1981); Zijp (2001)

633 157 000 Spitzer and ten Bosch (1977)

633 42‡ 32 000‡ Spitzer and ten Bosch (1975)

5 300 – 14 280†* Ko et al. (2000)

15

As most laser-tissue interactions are thermal in nature, the optical-to-thermal energy conversion

reactions following photon absorption and the subsequent non-radiative heat conversion,

propagation/decay and tissue responses are important physical parameters to consider. Thermal

parameters include thermal diffusivity (α) and thermal conductivity (κ), which refer to the rate

and amount of heat diffusion through a medium, respectively. Thermal diffusivity is an

important thermophysical parameter given by:

C

, (1)

where α is the thermal diffusivity, κ is the thermal conductivity, ρ is the density and C is the heat

capacity. Investigations reporting thermal properties of sound and carious enamel and dentin are

scarce. Furthermore, of those investigations, majority, if not all, are concerned with the

properties of sound enamel. A list of parameters derived from published literature is presented in

Table 2. Direct measurements of thermal conductivity and diffusivity are difficult to assess in

intact samples as well as thin slabs. Measurements are often carried out using thin enamel

sections and thermocouples. Considering that enamel and dentin sectioning can induce cracks,

defects or other anomalies which all significantly affect optical and thermal properties, being

able to extract optical and thermal parameters from whole teeth non-destructively would be

invaluable.

Table 2. Published set of thermal properties of sound and carious enamel.

* Carious sample

ffi Compressed hydroxyapatite powder

Thermal Properties of Enamel

Thermal Conductivity, κ *W/m·K+

Thermal Diffusivity, α *m2/s]

References

0.65 Soyenkoff et al. (1958)

0.87 Saitoh et al. (2000)

0.88- 1.07 Craig and Peyton (1961)

0.90/0.72* El-Brolossy et al. (2005)

0.93 4.7 x 10-7 Brown et al. (1970)

0.77 3.22 x 10-7 Minesaki (1990)

0.88 4.69 x 10-7 Braden (1985)

0.93 4.1 x 10-7 Barker et al. (1972)

0.92 4.2 x 10-7 Braden (1964)

4.09 x 10-7 O’Brien (1997); Panas et al. (2003)

2.27 x 10-7 Panas et al. (2003)

4.0 x 10-7‡ Rodriguez et al. (2001)

16

1.6.2 Microradiography

The most common microradiographic method is transverse microradiography (TMR) (Arends

and ten Bosch 1992). TMR is a destructive analytical technique that yields the most detailed

quantitative information to date (Damen et al. 1997). It provides direct measurements of the

mineral content of the examined dental tissues. In TMR, samples are cut into thin slices and

oriented perpendicularly to the anatomical tooth surface. The sections are placed on a piece of

high-resolution radiographic film and together with an aluminum step-wedge are irradiated with

monochromatic x-rays. X-ray absorbance shown by the optical density of the developed film can

be used to calculate two different parameters, mineral loss (vol%.μm) and lesion depth (μm)

(Arends and ten Bosch 1992). As enamel or dentin is treated with demineralizing solutions lesion

depth and mineral loss values increase, whereas both parameters are reduced upon

remineralization. The main setback of TMR is its destructiveness and tedious procedure of

sample sectioning and preparation. A recent advancement in the TMR software allows for the

accurate determination of mineral content in curved tooth surfaces by an algorithm that

mathematically flattens the section (de Josselin de Jong and van der Veen 2007). This is

completed through several scans of the microradiographed section and avoids additional sources

of error in mineral loss and lesion depth calculations and their overestimation due to the natural

curvature of tooth surfaces. Damen et al. (1997) judged TMR as the current ―gold standard‖ and

an appropriate tool for quantifying minor changes in mineral density over time.

1.6.3 Optical fluorescence techniques

Recently evolving methods of caries detection, utilize light sources as a tool to indirectly assess

the state of a tooth‘s health, or level of mineral loss. Considering the ordered structure of enamel

prisms and dentinal tubules, light, in the visible and near infrared part of the electromagnetic

spectrum, is able to propagate fairly well through teeth (Hall and Girkin 2004). As a result,

disruptions in the regular pattern of a tooth, i.e. a carious lesion or any other anomaly, will create

discontinuities within the medium, leading to enhanced light scattering and an alteration of the

optical path lengths. In addition to scattering, absorption and fluorescence properties may

likewise be altered by the presence of defects. Fluorescence is the phenomenon whereupon

electrons are excited from a ground or lower energy state to a higher energy state, and upon de-

excitation results in the emission of energy as longer wavelength light (Tranæus et al. 2005).

17

Although, some of the inherent fluorescence, or autofluorescence, of teeth can be attributed to

chromophores, the material responsible for the fluorescent properties remains uncertain (Stookey

2005). Thus, the baseline fluorescence of sound teeth may be a result of the combination of

inorganic matrix with absorbing organic molecules (Hibst and Paulus 1999).

Two non-destructive optical techniques that take advantage of fluorescence emission are

Quantitative Light-induced Fluorescence (QLF) and DIAGNOdentTM

.

1.6.3.1 Visible light Fluorescence- QLF

QLF is an optical fluorescence technique that distinguishes carious from non-carious regions

based on fluorescence radiance, which is lower in demineralized lesions (Angmar-Månsson and

ten Bosch 2001). Instruments using optical fluorescence, like QLF imaging, capture images of a

tooth by illuminating with blue-violet light from an arc lamp, which emits, with a wavelength of

370nm, white light filtered through a blue-transmitting filter based on xenon gas excitation and

emission technology. The basis of the technology is that demineralized areas will fluoresce less

than sound enamel and this difference is quantified as the fluorescence loss parameter, Q. The

cause of fluorescence loss was proposed to be due to 2 sources. The first is the presence of

chromophores, where in a demineralized area protein chromophores will be removed, resulting

in a loss in autofluorescence. The second source is due to the light scattering and absorption

properties of a healthy versus demineralized area (Stookey 2005). Due to the enhanced light

scattering properties found in demineralized lesions, the path of the light traveling within the

enamel is much shorter, compared to healthy enamel, and as a result the smaller amount of

absorption per volume yields lower fluorescence values. Furthermore, the scattering within

demineralized lesions creates an obstruction which prevents light travel from the fluorescing

dentin to the surface and excitation light from the surface to the dentin (Tranæus et al. 2005;

Angmar-Månsson and ten Bosch 2001). QLF has been demonstrated both in vitro and in vivo to

be sensitive to smooth-surface caries (Shi et al. 2001), occlusal caries (ten Cate et al. 2000),

secondary caries (Ando et al. 2004) and root caries (Gonzalez-Cabezas et al. 2001), while

attaining values of sensitivity and specificity from the aforementioned studies of no lower than

0.76 and well above 0.78, respectively. QLF, is, however, limited by its penetration depth to ≈

400 μm (Tranæus et al. 2005). Amaechi and Higham (2002) demonstrated the efficacy of QLF as

18

a tool to detect and longitudinally monitor the progression of artificial caries-like lesions and

their subsequent remineralization. Potential disadvantages of the QLF system are derived from

the fact that dehydration can significantly affect lesion fluorescence, putting into question the

clinical interpretation of the fluorescence values (Al-Khateeb et al. 2002, Pinelli et al. 2002).

Furthermore, repositioning the QLF probe at the same measurement point for longitudinal

monitoring of lesions was found to be challenging, especially when lesion parameters change

over time. Lastly, QLF is unable to accurately detect lesions interproximally (Pretty et al. 2002).

1.6.3.2 Laser fluorescence—DIAGNOdentTM

The type of fluorescence emission depends on the wavelength of the source light. Blue

fluorescence and yellow-orange fluorescence are emitted from incident light sources in the near-

ultraviolet region and in the blue-green region, respectively. The third type of fluorescence is red

fluorescence, where incident light is in the red or near-infrared region (Tranæus et al. 2005). A

device called DIAGNOdentTM

(DD) takes advantage of the red fluorescence by emitting light in

the visible-red region (λ = 655 nm) to induce red and near-infrared fluorescence, which is

collected by a photodiode combined with a long pass filter (transmission > 680 nm) as the

detector. The DD device involves point measurements given on a linear scale and presented on

the display screen as an integer between 0 and 99 (Pretty 2006). The nature of red fluorescence

has been attributed to different protoporphyrins that are present as bacterial breakdown products

and metabolites for other oral bacteria. The exact mechanism by which DD monitors incipient

caries has not been fully elucidated. However, due to the nature of red fluorescence, the DD

readings appear to be based on bacterial porphyrins rather than enamel mineral dissolution

(Pretty and Maupomé 2004; Astvaldsdottir et al. 2010). While DD had demonstrated greater

sensitivity compared to traditional diagnostic methods (visual inspection, radiography), a greater

prospect of encountering false-positive diagnoses has limited its clinical usefulness. For

example, DD readings have been found to be complicated by factors such as stains, plaque and

tooth hydration levels and over-scored due to disturbances in tooth mineralization as a result of

developmental hypomineralization (Ferreira Zandoná and Zero 2006). Disadvantages in the DD

system are related to the aforementioned high incidence of false-positive diagnoses. In

accordance with all other optical techniques, the presence of stains will highly confound the

19

technique (Hall and Girkin 2004). In addition to stains, calculus, plaque, some composite resin

filling materials, remnants of polishing pastes and developmental anomalies can all affect the

device readings leading to false-positive diagnoses (Pinelli et al. 2002, Lussi et al. 1999, 2005,

Shi et al. 2001). As a result, DD readings, should not solely be the basis for primary clinical

diagnosis, but rather should be used as adjuncts to current diagnostic tools.

1.6.4 Optical Coherence Tomography

Optical coherence tomography (OCT) is a non-destructive optical imaging technique based upon

light interference within semi-transparent materials, such as teeth. This methodology has been

developed and used in the field of opthamology for over a decade in addition to applications in

imaging of skin and gastrointestinal tissues (Hall and Girkin 2004). The OCT system illuminates

the teeth at 850 nm or 1310 nm wavelengths, which result in an optical imaging depth of 0.6 – to

2.0 mm, respectively. Through near-IR illumination of the tooth, a combination of high spatial

resolution (≈10-20 μm) and real-time 2-D depth visualization can be acquired (Amaechi 2009).

An OCT system contains a Michelson interferometer that splits the incident light beam into 2

coherent beams of light, the sample beam and the reference beam. The sample beam will enter

the tissue and scatter both in the forward and back direction, where the scattering properties are

dependent on anomalous structures and changes in refractive index within the tissue. The back

scattered sample beam is recombined with the reference beam and the generation of interference

patterns are observed by a photodetector. The intensity of the generated interference pattern is a

function of the scattering and caused by changes within the tooth structure (Hall and Girkin

2004). Generating a depth profile at a single point along the laser trajectory depth from a single

point on the tooth surface is referred to as an A-scan (Choo-Smith et al. 2008). Taking several A-

scans as a function of position along a line produces information from the assembled adjacent A-

scans in order to optically slice the tooth tissue, producing a 2-dimensional depth image referred

to as a B-scan (Hall and Girkin 2004). As conventional OCT systems were found to be highly

susceptible to the strong surface reflection from the high refractive index enamel, a modification

of the system to produce polarization-sensitive OCT (PS-OCT) was developed and uses linearly

polarized light which does not depolarize from surface reflection (Jones and Fried 2006). The

PS-OCT system had been successfully implemented to image artificial and natural caries lesions

and assessed severity in terms lesion depth in enamel (Fried et al. 2002) and the severity of

20

demineralization on dentin surfaces (Manesh et al. 2008). Furthermore, additional studies have

demonstrated that PS-OCT can image fluoride-enhanced surface layer remineralization in

enamel (Jones and Fried 2006) and remineralization of dentin (Manesh et al. 2009). OCT is still

too sensitive to natural crystal defects in enamel and produces a non-zero reflection baseline

which compromises its sensitivity to detect caries.

1.6.5 Photothermal Radiometry and Modulated Luminescence

Following initial absorption events within a medium, atoms or molecules are raised to excited

electronic states. Common modes of de-excitation processes involve a series of either radiative

transitions/decays, resulting in the production of longer wavelength light, fluorescence, and non-

radiative transitions which result in the production of heat. The basis of frequency-domain

photothermal radiometry (PTR) relies on the conversion of absorbed optical energy into thermal

energy, and the subsequent observation of modulated mid-infrared emission (Fig. 8). A periodic

heat source, such as an intensity modulated laser beam, results in the generation of a periodic

temperature distribution within a material. This oscillatory temperature field arising within each

light-absorbing layer of a material launches temperature waves known as ‗thermal waves‘ which

rapidly decay over the sample depth. Thermal waves are very heavily damped with decay

constants equal to the thermal diffusion length (Almond and Patel 1996). The thermal diffusion

length is a quantity given by equation (2):

ff

(2)

where α is the thermal diffusivity (given in equation 1) and f is the modulation frequency. The

thermal diffusion length is indicative of the depth penetrability of a thermal wave technique

analogous to the optical absorption depth of electromagnetic waves. It is clear from the formula

of the thermal diffusion length, that there is a strong dependence of the thermal diffusion length

on the thermal properties of the medium, more specifically thermal diffusivity (α), and laser

modulation frequency. Thus, a high diffusivity material, or low modulation frequency will

effectively enhance propagation and capture of thermal waves deeper into the medium. In

metals, optical absorption depths are limited to the nanometer scale resulting in heat generation

at the surface of the metal diffusing into the bulk. Therefore, conductive heat transfer dominates

21

and thermal diffusion lengths are much larger than optical penetration depths. This underscores

the sensitivity of photothermal techniques to the inspection of optically opaque materials well

beyond the range of optical imaging devices. In non-metallic polycrystalline materials, such as

teeth, the case is much different. Longer optical absorption depths mean that absorption

processes are not limited to the surface and as a result photothermal effects cannot be considered

as a simple surface heat source. As optical absorption depths are longer, elemental heat sources

can arise within the bulk of the medium. Thus, thermal wave generation within the bulk of an

optically-absorbing semi-infinite translucent material will depend on both optical absorption

processes, in addition to the thermal diffusion length. The resultant PTR signal is derived from

optical absorption and thermal wave generation, which creates a modulation in the temperature

of the sample surface by integrating all contributions over the depth of the sample (Almond and

Patel 1996).

Thermal contributions to the overall PTR signal are generated in 2 distinct modes, conductively

and radiatively. The conductive component dominates in the near-surface regions of a sample, as

described above, and is a function of the thermal properties of the sample and the laser beam

modulation frequency. The radiative component, a function of the longer penetration depth of the

diffusively scattered optical field, will also influence IR signal generation. An enhanced radiative

component, providing information from deep subsurface structures, originates in optically

absorbing and thermally-emitting subsurface features like incipient carious lesions (Jeon et al.

2004a). From a single PTR scan, the generated amplitude and phase signals and the improved

signal-to-noise ratio (SNR) due to lock-in detection (Mandelis 1994) increases the amount of

information gathered, compared to time-domain methods, which is the prominent feature of

frequency-domain techniques.

22

Figure 8. Photothermal and luminescence effects upon excitation with an intensity modulated

laser beam.

As mentioned above, PTR involves the monitoring of IR emissions using mid-IR detectors.

However, where the IR signal is collected depends on individual experimental methods. The

observation point on the sample can occur in 2 modes. Light excitation and IR emissions

collected from the same surface are referred to as ‗backscattered PTR‘ whereas excitation and

collection of IR emissions on opposite surfaces is referred to as ‗transmission-mode PTR‘.

As a complementary signal channel, modulated luminescence (LUM) monitors the optical-to-

radiative energy conversion, where photon absorption and excitation to a higher-energy state is

followed by de-excitation to a lower energy state and emission of longer wavelength photons

(Fig. 8). As a purely optical technique the high scattering coefficients of sound and carious

enamel and dentin significantly limit optical penetration depths. Investigation of the modulated

luminescence signal from enamel samples revealed the existence of a long (≈ ms) and short (≈

μs) relaxation lifetimes, the longer of which was present in all teeth and is insensitive to the

overall health of a tooth. In contrast, the shorter lifetime established a degree of sensitivity to the

quality of enamel (Nicolaides et al. 2002).

The combination of PTR and LUM amplitude and phase signals provides four sensitive channels

to assess the physical condition and the state of health of teeth. Changes in enamel and/or dentin

mineral density and porosity, characteristic of de-and re-mineralization processes, will alter the

optical and thermal properties of the tissue and the resultant mid-IR emissions. PTR-LUM has

demonstrated the ability to explore up to 5 mm below the enamel surface and provide

information regarding minor subsurface perturbations (Jeon et al. 2004a). PTR-LUM has been

23

shown to have the potential to detect and longitudinally monitor early interproximal

demineralization (Jeon et al. 2007), pit and fissure caries (Jeon et al. 2004), and artificial

demineralized and remineralized carious lesions on roots and enamel of human teeth (Jeon et al.

2008). The continual development and enhancement of the PTR-LUM system as a laboratory

investigation device has been investigated for nearly a decade at the Centre for Advanced

Diffusion-Wave Technologies, at the University of Toronto. A clinical prototype based on PTR-

LUM phenomena is currently in development by Quantum Dental Technologies, marketed as

The Canary Dental Caries Detection System.

Thanks to the development of PTR to detect thermal waves along with its strong, comprehensive

theoretical underpinning, describing the generated thermal signal inside a sample, the extraction

of optical and thermophysical material properties have been made possible. PTR measurements

have been used previously for depth analysis and non-destructive extraction of optical and

thermal properties from opaque materials (Tam 1985). Furthermore, in layered materials, PTR

has been used to investigate changes in the thermal properties of specific subsurface layers

(Balageas et al. 1986). In terms of teeth, PTR in its pulsed-mode has been investigated toward

the evaluation of optical absorption coefficients of enamel (Zuerlein et al. 1999; Zuerlein et al.

1998) and dentin (Chebotareva et al. 1993) at tooth ablation wavelengths (9-11 µm). In contrast

to frequency-domain PTR, the pulsed mode has only a single channel available, formed from the

rapid temporal decay of the thermal pulse (Nicolaides et al. 2001). Earlier reports on frequency-

domain PTR measurements introduced a robust and complex fitting algorithm for the generation

of independent sets and simultaneous extraction of optical and thermal parameters and thickness

values for the each effective layer considered in the 3-layer tissue analysis (Matvienko et al.

2009a/b). The robustness of the algorithm i.e., its independence of the initial estimation of

parameters, is an extremely important parameter in defining a unique solution in the multi-

parameter fitting procedure (Matvienko et al. 2009b).

In summary, combining the depth profilometric nature of PTR and the extraction of optical and

thermophysical properties from PTR data, this technique has been proven advantageous to

resolve the internal structure as well as characterize tissues thermophysically, in a non-contact,

non-destructive fashion.

24

2 Rationale

Dental caries is an infectious bacterial disease affecting mineralized tooth tissues, enamel and

dentin, characterized by loss of inorganic structure in subsurface layers (demineralization). Early

detection of this disease prior to cavitation, allows preventive therapies to be instituted by

promoting inorganic ion re-uptake (remineralization). The most studied therapeutic agent is

fluoride, with voluminous literature on the effects of fluorides in enhancing the remineralization

process. The influx of light and laser based caries detection systems, all pride on the unique

optical properties of teeth. Furthermore, in order to augment the effectiveness of each laser based

system, optical and thermal interactions between the laser and tissue volume must be

meticulously explored as changes in these properties may be reflective of the overall tooth

health. As enamel is a structurally and chemically composite tissue, the process of optical and

thermal property extraction is both technically challenging and computationally extensive,

typically involving destructive analysis of thin tissue sections.

As an emerging non-destructive technique, frequency-domain photothermal radiometry (PTR) is

an established sensitive methodology to characterize pathological dental tissues. PTR is based on

the generation of diffuse-photon-density waves in turbid media by a harmonically modulated

laser beam to induce an oscillatory temperature thermal-wave field, which can be detected

remotely with mid-IR detectors. Modulated luminescence (LUM) monitors the optical-to-

radiative energy conversion, a complementary signal channel.

The purpose of the present study was to evaluate the ability of back-propagation and

transmission PTR-LUM to detect, longitudinally monitor and quantify simulated enamel

demineralized and remineralized lesions. The project is divided into 2 sections based on the

PTR-LUM detection mode. The first section is concerned with PTR-LUM in backscatter mode

where a combined theoretical formalism applied to the experimental PTR signals was used to

extract opto-thermophysical properties from the treated enamel. The second chapter investigates

PTR-LUM in transmission-mode where changes as a function of demineralization and

remineralization time were monitored in real-time without sample disruption.

25

Hypothesis:

The combined detection modes of PTR-LUM are efficacious in measuring and quantifying

mineralized layers generated through dissolution and mineral deposition reactions, characteristic

of demineralization and remineralization processes.

The objectives of the first study investigating PTR-LUM in backscatter mode are two-fold:

1. To identify a relationship between PTR-LUM amplitude and phase signals to histological

features of demineralized and remineralized lesions through microradiographic analysis

2. To develop a coupled diffuse-photon-density and thermal wave model for the extraction

of opto-thermophysical properties from PTR signals and relate these changes in

properties to morphological changes during de- and re-mineralization.

Overall, this study is important in establishing PTR-LUM as a novel combination analytical

technique for the non-destructive evaluation of mineralized multi-layered enamel and

quantitatively characterizing the fundamental processes governing enamel demineralization and

remineralization.

26

3 PTR-LUM Backscatter Mode: Materials and Methods

3.1 Sample Collection and Sterilization

Forty-two mature, permanent human molars extracted by dental professionals for orthodontic or

other surgical purposes were collected, debrided of all soft attached connective tissue and sealed

in plastic containers containing distilled water at 4oC until use. The study protocol was approved

by the University of Toronto Ethics Review Board (Protocol #25075). Samples were collected

from dental offices in the Greater Toronto Area. Samples were submitted to the University of

Toronto‘s Department of Environmental Nuclear Science Gamma Irradiation services for

sterilization prior to utilization. Irradiation took place in a gamma cell (type G.C.220) at a dose

of 4080 Gy and a gamma dose rate of 3.3 kGy/hr. Gamma radiation has been established as an

effective and acceptable sterilization method for the elimination of microbes from dental

specimens without significantly affecting demineralization and remineralization rates (Amaechi

et al. 1999).

3.2 Sample Preparation

All sterilized samples (n = 42) were mounted on LEGO® blocks in order to allow for precise

realignment of samples on the sample stage during subsequent measurements. A single region

per tooth (lingual/palatal surface) was selected and assessed visually to ensure no visible stains,

cracks or other surface imperfections were present. Lingual/palatal surfaces of maxillary and

mandibular molars were the selected sites for treatment and PTR-LUM measurements. These

surfaces were previously found to be more susceptible to acid dissolution with the least amount

of variability compared to labial/buccal surfaces (Tucker et al. 1998). All samples were sealed in

a chamber containing Petri dishes of distilled water to maintain ambient humidity conditions.

Samples were maintained in the humid chamber at all times, excluding the time when

measurements and treatments were being executed. Retaining the samples in the humid chamber

maintained ambient conditions in a thermodynamically stable state and preserved sample

hydration for the duration of the experiment. Prior to the first PTR-LUM scan, each sample was

covered in 2 coats of transparent, acid-resistant nail varnish on all surfaces excluding the enamel

surface delimiting a 6 mm X 6 mm treatment window.

27

3.3 Demineralization and Remineralization Treatments

Samples were randomly distributed into 4 treatment groups outlined in Table 3. The first

treatment group was only demineralized. Two samples, not included in the group 4 matrix, were

used strictly for theoretical analysis and were demineralized for 40 days. The demineralizing gel

was changed after 20 days. The remaining 3 treatment groups were subjected to a mineral

solution with variations in fluoride content; either no fluoride, low fluoride (1 ppm) or high

fluoride (1000 ppm), in the form of NaF. All demineralizing and remineralizing treatments were

conducted at room temperature and in sealed experimental tubes.

Table 3. Treatment groups for backscatter PTR-LUM (n = 40)

3.3.1 Demineralization

The demineralizing medium consisted of an acidified lactic gel containing 0.1M lactic acid

gelled to a thick consistency with 6% hydroxyethyl cellulose (HEC) and adjusted to pH 4.5 by

the addition of 0.1M NaOH (Amaechi et al. 1998). Samples incubated in demineralizing

solutions were left unagitated for the duration of the treatment period. Mounted samples were

inverted and immersed in individual Falcon tubes containing 30 mL of acidified gel. Samples

were demineralized for a period of up to 10 days, with sample interruption for PTR-LUM

measurements after 5 days and 10 days of acid exposure. Following demineralization, all

samples were rinsed under running distilled water for 2 minutes in order to remove any residual

adsorbed gel on the enamel surface. The teeth were dried in ambient air for 1 hour, followed by

incubation in the humid chamber until PTR-LUM scans were executed. The same procedure was

followed for PTR-LUM scans after 5 days of demineralization.

Treatment Group Demineralization treatment (days)

Remineralization treatment (days)

Sample Size

Group 1: No fluoride remineralization 10 28 10

Group 2: Low fluoride remineralization (1 ppm F)

10 28 10

Group 3: High fluoride remineralization (1000 ppm F)

10 28 10

Group 4: Demineralized only 10 ----- 10

28

3.3.2 Remineralization

The constituents of the remineralizing solution are outlined in Table 4 (Amaechi and Higham

2002). Individual experimental groups were exposed to a remineralizing solution for 4 weeks

formulated with different concentrations of fluoride, 0 ppm, 1 ppm and 1000 ppm F as NaF. The

pH of the remineralizing solution was adjusted to levels approximating natural saliva, pH 7.2.

Sodium carboxymethylcellulose (CMC) was added in order to increase the viscosity of the

remineralizing solution to a consistency comparable to natural saliva, while methyl-p-

hydroxybenzoate served as a preservative (Amaechi and Higham 2001). The remaining

compounds provided the inorganic components required for the remineralization process. The

main constituents of enamel mineral, calcium and phosphate, were added to the remineralizing

solution in the form of calcium lactate and phosphate complexes, respectively (Amaechi and

Higham 2001). Samples were inverted and immersed in 30 mL of solution, renewed every 5

days. Following individual treatments, samples were rinsed under running distilled water for 2

minutes and left to air dry for 1 hour. After drying, samples were placed in the humid chamber

until PTR-LUM scans were performed.

Table 4. Composition of the remineralizing solution.

3.4 PTR-LUM Experimental Setup

The experimental set-up is shown in Fig. 9. The PTR-LUM experimental setup is equipped with

2 semiconductor laser diodes mounted on a rotating stage, one emitting at 660-nm (Mitsubishi

ML101J27) and the other at 830-nm (Thorlabs, DL7032-001). A description of the laser

Remineralizing solution components Concentration (g/L)

MgCl 2 ·6H 2 O 0.03

K 2 HPO4 0.121

KH 2 PO4 0.049 KCl 0.625 Calcium lactate 3.85 Methyl - p - hydroxybenzoate 2.0 Sodium carboxymethylcellulose 0.4

Fluoride 0 or 1 or 1000 ppm NaF pH (adjusted with KOH) 7.2

29

parameters is given in Table 5. A diode laser driver (Thorlabs, LDC 210) triggered by the built-

in function generator of the lock-in amplifier (Stanford Research System, SR830) modulated the

laser current harmonically. The modulated infrared PTR signal from the tooth was collected and

focused by two off-axis paraboloidal mirrors (Melles Griot 02POA017, Rhodium coated) onto a

Mercury Cadmium Telluride (MCT) detector (Judson Technologies J15D12, spectral range: 2 to

12 μm, peak detectivity D* ≈ 5×1010

cm Hz1/2

W-1

at ca. 12 μm) operating at cryogenic

temperatures by means of a liquid-nitrogen cooling mechanism and with an active area of 1 mm2.

Before being sent to the lock-in amplifier, the PTR signal was amplified by a preamplifier

(Judson Technologies PA-101). For the simultaneous measurement of PTR and LUM signals,

under 660-nm irradiation, a lens (focal length: 100 mm) was placed above the two off-axis

paraboloidal mirrors such that there was no interference with infrared energy passage between

the off-axis mirrors. The collected modulated luminescence was focused onto a silicon

photodiode. A cut-on coloured glass filter (Oriel 51345, cut-on wavelength: 715 nm) was placed

in front of the luminescence photodetector to block laser light reflected or scattered by the tooth.

For monitoring the modulated luminescence, another lock-in amplifier (Stanford Research

System, SR850) was used. Both lock-in amplifiers were controlled by a computer via USB to

RS-232 port connections.

Table 5. Laser parameters for backscatter PTR-LUM measurements.

Laser wavelength

Optical output power (CW)

Operating current

Beam Size

659 nm 130 mW 140 mA 5.60 mm

830 nm 100 mW 200 mA 0.71 mm

670 nm* 500 mW 800 mA 0.59 mm

30

Figure 9. Experimental setup for backscatter-mode PTR-LUM study in experiment 1.

3.5 PTR-LUM frequency scans

Initial PTR-LUM scans were done before any treatment (baseline measurement) at the center of

each delineated window. Samples were removed from the humid chamber 20 minutes prior to

PTR-LUM frequency scans. A further 10 min elapsed with the sample placed under direct laser

incidence in order to achieve thermal stabilization. This standardized procedure was followed for

all PTR-LUM scans and based on the earlier observation that changes in optical properties,

shown as changes in fluorescence intensity, and the thermal properties, were negligible following

20-min of stabilization time for periods lasting less than 1 hour (Jeon et al. 2004; Al- Khatteb et

al. 2002; Gmur et al. 2006). The total drying time implemented in the present study was in-line

with previous in vitro reports employing a 30-min (Pretty et al. 2002a) to 45-min (Zhang et al.

2000). PTR-LUM frequency scans were completed for all samples at 2 different wavelengths,

660-nm and 830-nm. The de-focused 660-nm laser beam ensured one-dimensionality of the

induced photothermal field. A full frequency scan consisted of varying the laser modulation

frequency at a fixed sample position from 1 Hz to 1000 Hz. This frequency range was segmented

into 21 steps controlled by computer software (Labview, National Instruments, Austin, TX,

USA) to automatically increment frequencies sequentially. A total of 28 data points were

measured at each frequency for PTR. Only the latter 20 data points were averaged and recorded

by the computer program. The first 8 data points served as cut-off points allowing time for the

samples to stabilize following a change in modulation frequency. For LUM measurements, 40

data points were averaged and recorded with 15 cut-off points. A similar frequency scan

Pre-Amplifier

HgCdTe Detector

Lock-in Amplifier

Optical filter & Photodetector

Off-axis mirrors

Laser Driver Waveform

Sync. Signal

Laser Diodes (659nm, 830nm)

Slider

Rotational stage

Sample

3-axis translational stage

Computer

Internal

Generator Function

Amplifier Lock-in

31

procedure was performed for 830-nm laser irradiation; however, no LUM data were available.

Frequency scans were performed during the demineralization process after 5 and 10 days of

treatment, and after 2, 5, 10, 20 and 28 days from the start of remineralization.

To obtain meaningful information from PTR frequency scan data and remove any influence of

instrumental frequency response, the experimentally measured signals must be calibrated against

an opaque semi-infinite reference sample. The instrumental transfer function was calculated

using a thermally thick glassy carbon sample (diameter 40 mm, thickness 10 mm, Grade GC-

20SS Tokai Carbon Co., Ltd., Japan) with known thermal conductivity (κ) and diffusivity(α) (κ =

5.8 W/mK, α = 4.8 × 10-6

m2/s). The measured glassy carbon PTR frequency response,

Vcarbon(ω), was fitted to the theoretical signal calculated for the semi-infinite opaque solid

[Mandelis 2001]:

0carbon carbon

0 0 0 0

, exp

2 1

s

s s

s s

IV C T z dz C z dz

kk

k

where k is the thermal conductivity, σ the thermal-wave number and I0 is the incident laser

intensity. Subscripts 0 and S refer to air and carbon glass, respectively. Obtained from the fits

was the only unknown parameter in the equation above, the instrumental factor, C(ω), and

subsequently used to normalize PTR experimental data. Experimental PTR amplitude and phase

signals were subsequently divided and subtracted from the theoretically derived instrumental

normalization factor, respectively. LUM transfer function was determined by reflecting the

incident laser light directly onto the photodiode using a mirror. The reference was divided and

subtracted from experimental LUM amplitude and phase, respectively.

3.6 Theoretical Model

In the present study, experimental PTR amplitude and phase signals were fitted to the 3-layer

coupled diffuse-photon-density-wave and thermal-wave theoretical model using simplex

downhill algorithm developed for the investigation of multilayered sound and demineralized

enamel (Matvienko et al. 2009b, 2009c) (Fig. 10). The theoretical model consisted of 2

components, the optical field and thermal field. A list of parameters in the theoretical fitting

32

program is listed in Table 6. The following theoretical model was derived by Dr. A. Matvienko

in communication with Prof. A. Mandelis.

Table 6. The list of parameters fitted from the theoretical analysis.

3.6.1 Optical Field

The optical field is generated by incident laser radiation and induces both coherent and diffuse

photon density fields within enamel, which make up the total diffuse photon density field:

; ; ;i i it c dz z z (3)

where ic is the coherent photon density and

id is the diffuse photon density of the turbid

medium. The subscript i denotes the effective layers where layer 1 – intact surface layer, layer 2

– lesion body and layer 3 – sound enamel.

The one-dimensional coherent photon-density field takes into account the reduction of the

incident intensity due to scattering and absorption (Matvienko et al. 2009c):

Symbol Parameter Units

μa Absorption coefficient m-1

μs Scattering coefficient m-1

α Thermal diffusivity m2/s

κ Thermal conductivity W/mK

ηNR Non-radiative energy conversion efficiency

μIR Infrared absorption coefficient m-1

H Heat transfer coefficient W/m2K

g Cosine of the scattering angle

L Layer thickness μm

R2 Reflection coefficient (reflection at L1 - L2 interface)

R3 Reflection coefficient (reflection at L2 - L3 interface)

33

1 1

1

1

1 2 2

2

1 2

1

3

0 1 2 1

1 2 1

0 1 2 1 2 3 2 1

1 2 1 2 3 2

0 1 2 3 1

1 exp exp 2

1 exp 2

1 1 exp exp exp 2

1 exp 2 1 exp 2

1 1 1 exp exp

t t

c

t

t t t

c

t t

t

c

I R z R L z

R R L

I R R L z L R L z L

R R L R R L

I R R R L

2 3

1 2

2 1 2

1 2 1 2 3 2

exp

1 exp 2 1 exp

t t

t t

L z L L

R R L R R L

(4)

where I0 is the laser intensity, R1 , R2 and R3 are the reflection coefficients of the outermost

turbid medium, the second layer, and the third layer interface, respectively .

Furthermore,

i i it a s (5)

where t is the total attenuation coefficient of layer i, which includes the absorption and

scattering coefficients of the medium.

Figure 10. The 3-layer geometrical representation used for theoretical analysis and associated

optical and thermal parameters of each layer.

The dc form of the diffuse-photon-density field [Nicolaides et al. 2001]:

2

2

13 '

i i i id a t d i

i

dz z G z

dz D (6)

where the function Gi and the reduced attenuation coefficient (µt‘) are given by:

i i

i i

i i

t i a

i s c

t s

gG z

g

and

(7)

' 1t a sg

(8)

Laser beam

L1 L2

0 L1 z

L3

L1 + L2

μa1 μs1 α1 κ1

R2 R3 R1

μa2 μs2 α2 κ2

μa3 μs3 α3 κ3

L1 L2

34

The general solutions for the optical fields for each layer (i = 1,2,3), including coherent and

diffuse components, can be written as:

1

1 1

1 1 1 1

1 2 1

exp exp

1 exp exp 2

t

eff t t

z a Q z b Q z

I C z R L z

(9a)

2

1 2 2 2

2 2 1 2 2 1

2 1 3 2 1

exp exp

1 exp exp 2 (

t

eff eff t t

z a Q z L b Q z L

I I C z L R L z L

(9b)

3

1 2 3 3

3 3 1 2

3 1 2

exp

(1 )exp

t

eff eff eff t

z b Q z L L

I I I C z L L

(9c)

where the integration constants due to the coherent field solutions are given by:

1

1

1

2

2

3 2

2

0 1

1 2 1

2 1

2 3 2

3 2

3,

3 '

1

1 exp 2

1 exp

1 exp 2

1 exp

i i i

i

i i i

s t a

a t t

eff

t

t

eff

t

eff t

gC

I RI

R R L

R LI

R R L

I R L

(10)

In Eqs. (9) Qi are defined as 3 'i ii a tQ . The third-kind boundary conditions at the air-tooth

interface and the continuity of photon-density field and photon flux at the interfaces between

solid layers are applied:

1 1

1 2

1 2

1 1

2 3

2 3

1 2 1 2

0

1 1

1 2

1 2 1 2

2 3

) 0

)

)

)

)

d d

z

d d

d d

z L z L

d d

d d

z L L z L L

da A z

dz

b L L

d dc D z D z

dz dz

d L L L L

d de D z D z

dz dz

(11)

The constant A is defined as, 12

1

rA D

r

(12)

35

where r is the internal reflection of uniformly diffusing radiation, which depends on the index of

refraction of the sample.

Solving the system of the five equations of the boundary conditions using the photon diffusion

and coherent fields, one can obtain the coefficients a1, a2, b1, b2, b3:

1

1

2

1

1 1 1 12 12

1

12 12 1 1 12 12 1 1

1 1 1 1 1

2 2 22 2 2 2 12 1 1 1 12 1 1 1

12 1 1 1

2 12 1 1 1

2 ( exp 2 ) 1 2;

1 2 exp 1 2 exp

exp 2 ;

exp 2 exp exp

exp ;

exp

t

t

t

t

VF G f N L d P X VXa

X VX Q L M X VX Q L

b a M d P f N L

a b Y f L d X a Q L X b Q L

Y f d L

b VF VX a Q L V

2 2

12 1 1 1

3 2 23 2 2 2 23 2 2

23 2 2 23 2 2 33 3

exp ;

exp exp

exp exp ;t t

X b Q L

b a X Q L b X Q L

Y d L Y f L Y d

(13)

Here, the parameters M, N, P, X, Y, and d are defined as:

1 1

1 2 1

3 1 2

1

1 1 1

1 1 1 2 2 2 1

3 2 1 2

1 11, , ,

1 1 1

, ,

, , 1 exp ,

1 exp .

i

t t

i ti iij ij

j j j j

eff eff t

eff t t

A AQ AM N P

Q A Q A Q A

DD QX Y

D Q D Q

d C I f d R d C I R L

d C I R L L

(14)

The coefficients F, G and V are defined as:

2 2

2 1

1 1 2

2 23 2 23 3 33

2 2

2 2 23 2 2 23 2 2 23

22 2 2 2 12 1 1 1

1 12 1 1 12 1 2 22 2 22 2

23

23

exp 1 exp 1 1

exp 1 exp 1 exp 1

exp 2 exp exp ;

1 exp 1 exp 1 1 exp 2 ;

1

11 ex

1

t t

t t

t t t

L Y L Y d YF d f

Q L X Q L X Q L X

Y f L d Y f d L

G d Y L f Y L d Y f Y L

VX

X

2 2

;

p 2Q L

(15)

36

3.6.2 Thermal Wave Field

The total photon density field (ψt) is also the source for the thermal wave field which propagates

as thermal waves into the medium. The thermal wave field is given as:

2

2

2; ; ; 1,2,3i

i

a

i i i NR t

i

dT z T z z i

dz

(16)

where i

i

i

(17)

is the thermal wavenumber, [m-1

], which depends on the modulation frequency and on thermal

diffusivity of i-th layer.

The thermal-wave fields for each layer can be written in the form:

1 1

1 1 1 1 1 1 1 1 1

1 1 1

; exp exp exp exp

exp exp 2 ;t t

T z A z B z C Q z D Q z

E z F L z

(18a)

2 2

2 2 2 1 2 2 1 2 2 1

2 2 1 2 1 2 2 1

; exp exp exp

exp exp exp 2 ;t t

T z A z L B z L C Q z L

D Q z L E z L F L z L

(18b)

3

3 3 3 1 2 3 3 1 2

3 1 2

; exp exp

exp ;t

T z B z L L D Q z L L

E z L L

(18c)

The coefficients Ci, Di, Ei and Fi are defined as:

1 1

1

1

2 2

1 2

2

3 3

1 32

3

1 1

1

1

2 2

2 2

1 12 2

1 1

2 22 2

2 2

3 32 2

3 3

1 12 2

1 1

; 1, 2

; 1,2,3

1 ;

1 ;

1 ;

1

i i

i i

NR a

i i

i i i

NR a

i i

i i i

NR a

eff

t

NR a

eff eff

t

NR a

eff eff eff

t

NR a

eff

t

C a iQ

D b iQ

E I C

E I I C

E I I I C

F I C

2 2

1 2

2

2

2 2 32 2

2 2

;

1 .NR a

eff eff

t

R

F I I C R

(19)

37

To determine the coefficients Ai and Bi, the following boundary conditions are used:

1 1

1 2 1 2

1

1 1

0

1 1 2 1

1 2

1 2

2 1 2 3 1 2

2 3

2 3

,) 0; ;

) , , ;

, ,) ;

) , , ;

, ,) .

z

z L z L

z L L z L L

dT za HT

dz

b T L T L

dT z dT zc

dz dz

d T L L T L L

dT z dT ze

dz dz

(20)

The photothermal radiometric (PTR) signal represents the overall Plank radiation emission

integrated over the depth of the sample:

1 2

1 20

, , ,IR IR IR

L L

z z z

PTR IR

L L

V C T z e dz T z e dz T z e dz

(21)

Here, μIR is the spectrally averaged infrared absorption/emission of the medium. The IR

absorption spectrum for enamel is shown in Fig. 7B.

The measured PTR signal has an oscillating character and can be represented as:

exp PTRi

PTR PTRV V

, (22a)

where the amplitude and phase components are:

PTR PTR,PTR PTRAmp V Phase (22b)

3.7 Multiparameter Fitting of Experimental Curves

Experimental frequency scan data were fitted across the frequency range of 4 Hz – 354 Hz. At a

modulation frequency of 4 Hz the assumption of no dentinal involvement is based on the

determination of the thermal diffusion length of intact enamel. Given the lowest modulation

frequency of 4 Hz and a range of previously published values of the thermal diffusivity of sound

enamel (α = 4.0 - 4.69 x 10-7

m2/s) (Braden 1964), the thermal diffusion length (see equation 2)

is approximately μ (4 Hz) ≈184 µm, much smaller than the average thickness of lingual enamel

(≈0.84 – 2.04 mm) (Macho and Berner 1993). The assumption of one-dimensional heat diffusion,

38

i.e. heat loss due to lateral diffusion was negligible, was employed based on the size of the

illuminated area (Table 5) relative to the thermal diffusion length in the range of modulation

frequencies investigated. This was accomplished by defocusing and expanding the laser beam to

≈5.60 mm, a size much larger than the thermal diffusion length at the lowest modulation

frequency investigated (1 Hz).

For the theoretical representation of sound mature enamel, a 2-layer representation was assumed,

where layer 1 denoted a thin surface layer of finite thickness where mineral content and

optothermal properties vary from underlying sound enamel, henceforth referred to as

‗aprismatic‘ enamel, and layer 2 as semi-infinite enamel (Fig. 11). The properties of layer 2 and

layer 3 were equalized, as the underlying sound enamel substrate was considered semi-infinite.

By assuming a two-layer approximation of the three-layer model to fit the enamel data, the

complexity of the computational fits was significantly reduced in addition to the implementation

of the same mathematical description and software package for sound and demineralized enamel

(Matvienko et al. 2009b).

Figure 11. Schematic geometry of effective layers for multiparameter fittings of sound enamel.

All parameters were fitted between the limits defined in Table 7 for sound enamel or

de/remineralized enamel. The criterion for the best fits was defined by the residual, i.e. the

combined deviation between experimental and theoretical amplitude and phase curves. The

computational algorithm did not provide any restrictions to the fitting results and ‗selected‘ the

optimal values in the multi-parameter fitting procedure, such that values fell within the defined

limit ranges and did not converge to either the upper/lower limits in the range. The tolerance of

the fitting procedure represented the change in the residual corresponding to the change of a

single parameter. The fitting procedure continued until the change in any of the parameters

Aprismaticlayer

Sound enamel

0 L1 z

Laser beam

39

stopped decreasing the residual, defined by the tolerance, or until the maximum number of

iterations was reached, whereupon the algorithm stopped (Matvienko et al. 2009a).

The initial procedure involved fitting experimental frequency scan data from baseline

measurements, across the frequency range 4 Hz to 354 Hz, to the upper and lower limits of the

parameter ranges for sound enamel, as derived from literature (Table 7). A broader range of

upper and lower limits was fixed for layer 1 (aprismatic layer) as the physical characterization of

this layer has been omnipresent, however, in terms of optical and thermal parameters, properties

are undefined in the literature (Kodaka 2003; Ripa et al. 1966; Xue et al. 2009; Gwinnett 1967;

Whitaker 1982).

The initial fit on untreated enamel was performed by segmenting the range of limits into 20 - 30

equal steps and best fits were performed for all combinations and all parameters. The derived set

parameters from the initial fitting across the 20 – 30 division range were averaged and used as

input values (± S.D.) to perform a second fit across the same number of divisions (20 – 30)

between the limits. This averaging process was performed 3 times in order to derive a set of

optical and thermal parameters, independent of the number of divisions between the limits. It

was previously shown (Matvienko et al. 2009a) that the initial range of the parameters can be

significantly reduced (up to 100 times) through the averaging process to generate a narrow range

of unique values, from the best fits of the experimental data, which accurately describes the

properties of the sound enamel sample.

40

Table 7. Fixed upper and lower limits of the fundamental parameters defined for the

multiparameter fitting of untreated, sound enamel and de- and remineralized enamel.

Physical parameters Layer

Sound enamel De- and remineralized

enamel

Lower

limit

Upper

limit

Lower

limit Upper limit

Absorption coefficient

[µa, m-1

] L1 + L2 1 100

a 1 150

Scattering coefficient

[µs, m-1

]

L1 110b 6 000

a 110

b 157 000

d

L2 1 000c

6 000a 1 000

c 157 000

d

Thermal conductivity

[κ, W/mK]

L1 0.10 0.93e 0.10 0.93

e

L2 0.77f 0.93

e 0.10 0.93

e

Thermal Diffusivity

[α, m2/s]

L1 2.0 x 10-7 f

7.7 x 10-7

2.0 x 10-7 f

7.7 x 10-7

L2 4.2 x 10-7 g

7.7 x 10-7

2.0 x 10-7 f

7.7 x 10-7

Aprismatic layer

thickness [L1, µm] L1 5 60

* -------

a Fried et al.,[1995];

b Zijp, [2001] and references therein;

c Spitzer and ten Bosch, [1975];

d

Spitzer and ten Bosch, [1977]; e Craig and Peyton, [1961];

f Minesaki, [1990];

g Braden,

[1964]; * Kakaboura et al., [2005]. Sound enamel: L1 = aprismatic layer and L2= semi-

infinite sound enamel; Demineralized enamel: L1 = intact surface layer and L2= lesion body

The final derived set of sound enamel optical and thermal parameters was then fixed as

representing the properties for Layer 3 in subsequent fittings of demineralized and remineralized

treatment curves. Thus, the sound enamel curve was always the first curve fitted. From the first

exposure of the sample to the acid demineralizing gel, the 2-layer configuration of sound enamel

was no longer valid. As a result, the 3-layer profile was considered, where Layer 1 denoted the

intact surface layer overlying the demineralized lesion body (Layer 2), followed by semi-infinite

sound enamel (Layer 3) (Fig. 12).

Figure 12. Schematic structure of effective layers used for fits of demineralized and

remineralized enamel. L1 = surface layer; L2 = lesion body; L3 = sound enamel.

Surface layer

Lesion body

Sound enamel

0 L1 L1 + L2 z

Laser beam

41

The final demineralized PTR curve was fitted with thicknesses derived from TMR mineral

content profiles (Fig. 13). The lower limit for thickness of layer 1 was defined as the depth at

maximum content of the surface layer (MSL) and upper limit defined as the median between the

maximum content of the surface layer and minimum content of the lesion body (SLMAX). The

thickness limits of layer 2 were defined as the difference between LM (the median between the

lesion depth, LD, and the depth at the minimum content of the lesion body, MLB) and SLMAX, as

the lower limit; and difference between LD and the depth at MSL as the upper limit.

Figure 13. Schematic mineral content profile for the theoretical determination of layer

thicknesses. MSL denotes the maximum mineral volume of the surface layer. MLB refers to the

minimum mineral content in the subsurface lesion body. SLMAX refers to the upper limit of the

surface layer thickness, defined as the median between MSL and MLB. LM refers to one boundary

for the lower limit determination of lesion body thickness and defined as the median between

MLB and LD. LD refers to the TMR defined lesion depth at 95% of the sound enamel calibration

level (SE) at 87 vol%. L1 = intact surface layer and L2 = subsurface lesion.

After deriving layer thicknesses for layers 1 and 2, they were fixed as the upper limits for fitting

intermediate treatment curves. Therefore, all parameters, excluding thicknesses, were allowed to

vary between the limits defined in Table 7. The lower limit for thermal diffusivity was fixed at

the value determined for dentin (2.0 x 10-7

m2/s) (Minesaki 1990), whereas the upper limit was

fixed at the product of an 85% increase in the average thermal diffusivity from Table 2 (≈ 4.2 x

10-7

m2/s). The latter value was determined from preliminary investigations of parameter limits,

where fitted parameters varied freely between the defined limits without converging to the upper

limit. For the thicknesses the major assumption was that intermediate thicknesses were no larger

than the thicknesses derived at the treatment end point.

SE

87

vol.

%

LD SLMAX LM

Sample depth (μm)

MSL

MLB

L2 L1

42

For remineralized samples, final PTR curves following remineralization were fitted first in the

same manner as PTR curves following the last demineralization. All parameters were allowed to

vary between the limits defined in Table 7, except thicknesses, which were determined by TMR

mineral content depth profiles as described above and shown schematically in Fig 10. From

fitting the final remineralized PTR curve, the TMR-measured thicknesses of layer 1 and 2 were

fixed as the lower limit and upper limit for fitting the final demineralized PTR curve,

respectively. In this way, two treatment end points can be defined in fitting the intermediate

remineralized curves. The lower limit for layer 1 was set at 5 μm, which was the lower limit of

the aprismatic layer for fitting sound enamel. This was done in order to account for large

aprismatic layers that may decrease in thickness during the demineralization period. The upper

limit for layer 2, the lesion body, was set as the difference between the sound enamel level (SE)

and the depth at the surface layer maximum (Fig. 13). Following the derivation of parameters

corresponding to the 2 treatment end-points, with the final thicknesses based on TMR values,

thicknesses of both layers were fixed for fitting intermediate remineralization PTR curves.

The uniqueness of the fitted parameters is essential in verifying the reliability and robustness of

the theoretical algorithm. The uniqueness-of-fit to the multi-parameter computational algorithm

following de- and remineralization is demonstrated in Appendix 4.

3.8 Transverse microradiography (TMR) and image analysis

Following completion of all PTR-LUM measurements all samples were subjected to transverse

microradiography (TMR) analysis to determine the mineral loss and depth of the artificially

demineralized and remineralized lesions. Sample preparation and image analysis was completed

at the University of Texas Health Science Center at San Antonio, under the supervision of Prof.

B.T. Amaechi. The samples were sectioned using a water-cooled diamond-coated wire saw

model 3242 (Well, Le Locle, Switzerland), to produce a thin enamel slice approximately 100-µm

from the lesion area. A thin section was taken from the treated enamel region across the center of

the laser beam irradiation spot (≈5 mm). The slice, together with an aluminum step wedge (10

steps of 24.5 µm thickness), was microradiographed on type lA high resolution glass X-ray

plates (IMTECH CA, USA) with a Phillips x-ray generator system equipped with a nickel

filtered Cu-Kα target, producing monochromatic radiation of wavelength appropriate for

43

hydroxyapatite (l84 Ǻ). The plates were exposed for 10 minutes at 20kV/10 mA, and processed.

Processing consists of a 5-minute development in a developer (Kodak HR) and 15 min fixation

in a Rapid-fixer (Kodak) before a final 30-minute wash period. After drying, the

microradiographs were visualized using a DMR optical microscope (Leica) linked via a CCTV

camera (Sony, XC-75CE) to a personal computer (90 MHz Dell™ Pentium). The enhanced

image of the microradiograph was analyzed under standard conditions of light intensity and

magnification and processed, along with data from the image of the step wedge, using the TMR

software (TMRW version 2.0.27.2, Inspektor Research Inc., Amsterdam, Netherlands) (de

Josselin de Jong et al. 1987) to quantify the lesion parameters of integrated mineral loss (∆z,

vol%.µm) and lesion depth (LD, µm). The implementation of the latest dedicated TMR software

package utilized a new algorithm developed to mathematically flatten curved tooth surfaces, by

completing several scans for each microradiographed section. The mineral loss was computed as

the difference in volume percent of mineral between sound and demineralized tissue integrated

over the lesion depth. The mineral content plateau in deeper regions of the enamel section,

representative of sound tissue, was preset at the 87 vol% level (de Josselin de Jong et al. 1987).

The lesion depth was determined as the distance from the measured sound enamel surface to the

location in the lesion where mineral content was 95% of the sound enamel mineral volume.

Lesion parameters were determined by averaging several scans over the distance of the thin

section taken from the center of the treated area and corresponding to the irradiated beam size in

PTR-LUM experimental measurements.

3.9 Statistical analysis

Data obtained from TMR image analysis were analyzed statistically. Significant differences

between demineralized and remineralized lesions in terms of lesion depth and mineral loss in the

presence of variable fluoride concentrations were examined using ANOVA and post hoc Tukey‘s

test (p < 0.05). All statistical analysis was done using statistical analysis software (SPSS v. 14.0

for Windows, SPSS Inc., Chicago, IL).

44

4 Results

4.1 Sound enamel

4.1.1 Microradiographic Analysis and PTR-LUM signals

Intact, sound and untreated enamel surfaces exhibited a shiny, lustrous and semi-transparent

appearance, characteristic of healthy enamel (Fig. 14a). From the sound enamel samples (n= 4)

sectioned for TMR analysis average mineral loss and lesion depth parameters (± s.d.) were 322.5

± 162.8 vol%.µm and 19.8 ± 18.5 µm, respectively. Microradiographic images and associated

densitometric tracings for a representative sound enamel sample are presented in Fig. 15.

Microradiographs revealed uniform high radiodense enamel in all sound enamel samples. The

mineral volume profiles showed a thin surface layer of lower mineral volume, distinctly

identifiable from underlying bulk enamel. A gradual increase in mineral volume from the

anatomical enamel surface to bulk enamel occurred at a depth below the enamel surface, ranging

from approximately 4.4 µm to 44.0 µm.

Figure 14. Visual appearance of (a) sound enamel and (b) white-spot appearance after 10-days

of acid treatment.

PTR amplitude decreased across the entire frequency range from 1 Hz to 1 kHz with a notable

decrease in slope at frequencies above ≈44 Hz (Fig. 15). PTR phase exhibited near-linear

frequency dependence at modulation frequencies in the low-intermediate range (≈1 – 100 Hz).

The presence of phase maxima became apparent at modulation frequencies above 100 Hz. LUM

amplitude exhibited characteristic curvature and large slope changes in the mid-frequency range

(≈ 63 – 100 Hz) which were associated with the corresponding phase minimum.

(a) (b)

45

Figure 15. PTR-LUM amplitudes and phase curves for a representative sound enamel sample

under 660-nm laser excitation. The densitometric tracing (top right) and microradiographic

image (bottom right) are presented in the adjacent figures. Error bars, when not visible, are of

the size of the symbols.

4.1.2 Theoretical analysis of untreated enamel samples

Multiparameter fits of amplitude and phase signals generated from a representative sound enamel

sample showed very good agreement between experimental and theoretical curves (Appendix 2;

Fig. A.2.1). Theoretical fitting of sound enamel curves of multiple samples (n = 10) revealed a

narrow range of optical and thermal parameters of each layer as well as thicknesses of the

aprismatic enamel layer. A list of the central parameters derived from multi-layered sound

enamel is presented in Table 8. The mean derived thickness of layer 1 (aprismatic layer) was ≈13

µm. A derived set of parameters for layer 2 showed that they were distinct from layer 1 and

within the range of values derived from literature. While the range and standard deviations for

the aprismatic layer were rather high, there was a high degree of inter-sample reproducibility in

the derivation of sound enamel parameters (Table 8).

100µm

1 10 100 1000

1E-4

1E-3

PTR Amplitude

Am

plit

ude (

a.u

.)

Frequency (Hz)1 10 100 1000

0.10

0.12

0.14

0.16

0.18

0.20

0.22

0.24

0.26

LUM Phase

LUM Amplitude

Am

plit

ude (

a.u

.)

Frequency (Hz)

1 10 100 1000

-95

-90

-85

-80

-75

-70

-65

-60

-55 PTR Phase

Phase (

Deg)

Frequency (Hz)1 10 100 1000

-18

-16

-14

-12

-10

-8

-6

-4

-2

Phase (

Deg)

Frequency (Hz)

46

Table 8. Mean (± s.d.) derived optical and thermal parameters of intact enamel layers (n = 10)

4.2 Demineralization Group

4.2.1 Microradiographic Analysis and PTR-LUM Signals

Acid gel demineralization of intact samples produced visible white spot enamel lesions (Fig.

14b). Lesions were created with an average mineral loss and lesion depth of 1247 ± 502

vol%.µm and 90 ± 12 µm, respectively, determined from TMR measurements. A representative

demineralized lesion treated for 10 days is shown in Fig. 16. The lesion characteristics were

those of a classical subsurface lesion in which microradiographs defined a uniform, clear and

distinct lesion body underlying a superficial intact enamel surface layer with mineral volume

near, but lower than, the sound enamel level. Layer thickness determined by TMR analysis,

averaged at several points across the microradiographed lesion, were 3.6 µm for the surface

layer, and 85 µm for the lesion width, defined as the distance between the peak mineral of the

intact surface layer to the point where mineral volume is 95% of sound enamel level (Fig. 16).

PTR-LUM frequency scans are also shown in Fig. 16. PTR behaviour to subsurface lesion

formation exhibited increases in amplitude across the entire modulation frequency range. A large

PTR amplitude increase after 5 days resulted in slope changes in the frequency response and the

onset of curvature predominately at high modulation frequencies, as expected from the depth-

profilometric character of this technique (high modulation frequencies correspond to short

thermal diffusion lengths). After the 10-day treatment period, amplitude curvature shifted to

lower modulation frequencies. Inflection of the PTR phase of the demineralized curves with the

healthy curve occurred initially at higher modulation frequencies and shifted to lower

frequencies as treatment progressed. This resulted in a larger phase lag at high modulation

frequencies. As demineralization progressed, PTR amplitude increased in a monotonic fashion

while PTR phase curves exhibited a shift in maxima to lower modulation frequencies. This

resulted in an increase in phase lag at high frequencies and decrease in phase lag at lower

Sound enamel

Parameters Layer 1:

Aprismatic enamel Layer 2:

Sound enamel

Absorption coefficient (µa ; m-1) 65 ± 15 44 ± 23

Scattering coefficient (µs ; m-1) 763 ± 1113 5399 ± 847

Thermal conductivity (κ ; W/mK) 0.48 ± 0.23 0.87 ± 0.05

Thermal diffusivity (α; m2/s) 5.29 x 10-7 ± 1.45 x 10-7 4.41 x 10-7 ± 8.94 x 10-9

Layer thickness (µm) 13.41 ± 7.79 —

47

modulation frequencies. Trends similar to those detailed above were also observed in the

frequency response under the 830-nm laser (Appendix 1; Fig. A.1.1). The LUM signal channel

also exhibited consistent trends with treatment time for demineralized enamel. A monotonic

depression in both amplitude and a decrease in phase minima were evident. It is important to

note the opposite trends in the PTR and LUM signals during demineralization, where PTR signal

amplitudes increase with demineralization and LUM signals decrease.

An additional sample, not included within the demineralized control sample matrix, was treated

for an extended period of time (40 days) for theoretical analysis and is displayed in Fig. 17. The

40-day lesion exhibited similar histology to the 10-day lesion, although presented a deeper lesion

body and thicker intact surface layer (lesion depth = 114.8 µm). A distinct radiodense surface

layer is visible above a radiolucent body of the lesion. The same trends in PTR and LUM

identified above for the lesion displaying classical subsurface behaviour are also evident in the

current sample. Amplitude monotonically increased and phase lag monotonically decreased at

low modulation frequencies. After ≈10 days of treatment, PTR amplitude at high modulation

frequencies did not change much until the end of treatment, whereas an increase and pronounced

curvature were marked at lower modulation frequencies. A phase maximum shift to lower

modulation frequencies was also clearly evident over the duration of treatment. Interestingly,

after about 20 days of acid exposure, a secondary phase peak at ≈200 Hz became apparent.

Similar PTR amplitude and phase behaviour was noted in the frequency response under the 830-

nm laser (Appendix 1; Fig. A.1.1).

48

Figure 16. PTR-LUM amplitudes and phase curves for a 10 day demineralized sample under

660nm laser excitation. Error bars, when not visible, are of the size of the symbols. The

densitometric tracing (top right) and microradiographic image (bottom right) of the lesion are

presented in the adjacent figures. Mineral loss = 1310 vol%.μm; Surface layer thickness = 3.6

μm; Lesion width= 85.0 µm. Error bars, when not visible, are of the size of the symbols.

Enamel

100µm

1 10 100 1000

1E-5

1E-4

1E-3

0.01

Before Treatment

Demin - 5 days

Demin - 10 days

Am

plit

ude

(a.u

.)

Frequency (Hz)1 10 100 1000

0.1

0.15

0.2

0.25PTR Amplitude LUM Amplitude

Am

plit

ude (

a.u

.)

Frequency (Hz)

1 10 100 1000

-100

-95

-90

-85

-80

-75

-70

-65

-60

PTR Phase

Phase (

Deg)

Frequency (Hz)1 10 100 1000

-18

-16

-14

-12

-10

-8

-6

-4

-2

LUM phase

Phase (

Deg)

Frequency (Hz)

49

Figure 17. PTR-LUM signals for the 40 day demineralized lesion under 660-nm. Error bars,

when not visible, are of the size of the symbols. The densitometric tracing (top right) and

microradiographic image (bottom right) of the lesion are presented in the adjacent figures.

Mineral loss =1420 vol%.μm; Surface layer thickness = 2.6 μm; Lesion width= 112.2 µm. Error

bars, when not visible, are of the size of the symbols.

4.2.2 Theoretical analysis of demineralized enamel samples

Of the 17 parameters extracted from the theoretical fitting of demineralized samples, a select

group of parameters were found to change with treatment time, while no specific trends were

identified in the remaining parameters (See Appendix 3). The central parameters which changed

as a function of treatment time were the main optical and thermal transport properties, as

expected, including optical scattering and absorption coefficients, thermal conductivity and

diffusivity and layer thicknesses and are presented in Figs. 18 – 20. A sample exposed to the

demineralizing solution for 10 days, similar to substrates used for remineralization studies is

shown in Figs. 18 and 19a. A second sample was incubated for an extended period (40 days) in

the demineralizing agent, with PTR-LUM measurements at 0, 5, 10, 15, 20, 30 and 40 days

(Figs. 19b and 20). Both samples showed a good fit of experimental data to 3-layer theory at all

treatment times (Appendix 2; Fig. A.2.2).

1 10 100 1000

1E-4

1E-3

0.01

Am

plit

ude (

a.u

.)

Frequency (Hz)1 10 100 1000

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

Before Treatment

Demin- 5 Days

Demin- 10 Days

Demin- 15 Days

Demin- 20 Days

Demin- 30 Days

Demin- 40 Days

PTR Amplitude LUM Amplitude

Am

plit

ude (

a.u

.)

Frequency (Hz)

1 10 100 1000

-78

-75

-72

-69

-66

-63

-60

-57 PTR Phase

Phase (

De

g)

Frequency (Hz)100

-19.5

-19.0

-18.5

-18.0

-17.5

-17.0

LUM phase

Phase (

De

g)

Frequency (Hz)

1 10 100 1000

1E-4

1E-3

0.01

Am

plit

ude (

a.u

.)

Frequency (Hz)1 10 100 1000

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

Before Treatment

Demin- 5 Days

Demin- 10 Days

Demin- 15 Days

Demin- 20 Days

Demin- 30 Days

Demin- 40 Days

PTR Amplitude LUM Amplitude

Am

plit

ude (

a.u

.)

Frequency (Hz)

1 10 100 1000

-78

-75

-72

-69

-66

-63

-60

-57 PTR Phase

Phase (

De

g)

Frequency (Hz)100

-19.5

-19.0

-18.5

-18.0

-17.5

-17.0

LUM phase

Phase (

De

g)

Frequency (Hz)

100µm

50

The change in optical parameters (absorption and scattering coefficients) and thermal parameters

(diffusivity and conductivity) as a function of demineralization time for the 10 day treated

sample is shown in Fig. 18a-d. Over the 10 day period, absorption (Fig. 18a) and scattering (Fig.

18b) increased in the surface layer (layer 1). Within the lesion body (layer 2), little change in

absorption was found, whereas scattering increased linearly from the onset until the end of the 10

day period. Thermophysical properties of both layers, conductivity (Fig. 18c) and diffusivity

(Fig. 18d), became poorer with demineralization, excluding the thermal conductivity of the

surface layer which increased at day 10.

Figure 18. The change in optical absorption (a) and scattering (b) coefficients and thermal

conductivity (c) and diffusivity (d) parameters as a function of time, over the 10 day

demineralization period. Layer 1 = surface layer; Layer 2 = lesion body.

0 5 10

0

20000

40000

60000

80000

100000

120000

140000

160000

Sca

tte

rin

g C

oe

ffic

ien

t (m

-1)

Treatment Time (days)

Layer 1

Layer 2

0 5 10

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

The

rmal

Co

nd

uct

ivit

y (W

/mK

)

Treatment Time (days)

Layer 1

Layer 2

0 5 10

3.5x10-7

4.0x10-7

4.5x10-7

5.0x10-7

5.5x10-7

6.0x10-7

6.5x10-7

Th

erm

al D

iffu

sivi

ty (

m2/s

)

Treatment Time (days)

Layer 1

Layer 2

(c) (d)

(a) (b)0 5 10

70

80

90

100

110

120

130

Ab

sorp

tio

n C

oef

fici

ent

(m-1

)

Treatment Time (days)

Layer 1

Layer 2

51

Changes in layer thicknesses of the 10-day and 40-day demineralized samples are shown in Fig. 19. Over

the 10-day period, the thickness, or depth, of the growing subsurface lesion increased nearly linearly. At

later treatment times (Fig. 19b), the thickness of layer 2 continued to increase until the end of the 40-day

treatment period. In terms of layer 1, opposite behaviours were observed in the 2 presented samples. The

thickness of the surface layer decreased from 0 days over the 10 day period in Fig. 19a. In the 40 day

demineralized lesion (Fig. 19b), the thickness was stable for the first 15 days followed by an increase

until the end of the treatment period. The final thickness of layer 1 and layer 2 determined theoretically

for the 10 day sample were 6.6 µm and 81.2 μm, respectively. Final thicknesses determined theoretically

for the 40 day sample were 18.7 µm and 92.1 µm, respectively.

Figure 19. Changes in the thickness of layer 1 and layer 2 as a function of time for the 10 day (a)

and 40 day (b) demineralized samples. The inset in (b) shows the details of layer 1 thickness over

time on an expanded scale. Layer 1 = surface layer; Layer 2 = lesion body.

Optical and thermophysical properties plotted as a function of time for the 40-day demineralized

sample are shown in Fig. 20a-d. As in the 10-day demineralized sample, absorption and

scattering coefficients of layer 1 had an increasing trend over the demineralization period (Fig.

20a). After the 30-day period the scattering properties of the demineralized lesion body were

dominant and superseded the scattering properties of the surface layer. Thermal conductivity

(Fig. 20c) and diffusivity (Fig. 20d) of layer 2 decreased rapidly for the first 10 days of

demineralization reaching a minimum at 15 days after which properties slightly increased and

0 5 10

0

10

20

30

40

50

60

70

80

Layer 1

Layer 2

Laye

r Th

ickn

ess

(m

)

Treatment Time (days)0 10 20 30 40

0

10

20

30

40

50

60

70

80

90

0 10 20 30 40

10

12

14

16

18

20

Laye

r Th

ickn

ess

(m

)

Treatment Time (days)

Layer 1

Layer 2

(b)(a)

52

stabilized for the remainder of the treatment period. Thermal conductivity and diffusivity of layer

1 behaved similarly; a decrease over the first 15 days was followed by an increase above the

baseline level at day 0. Thermal diffusivity after 20 days increased nearly linearly until the end

of treatment.

A summary of the typical trends in the core physical parameters following demineralization are

presented in Table 9. The trends were evaluated from the 10-day (Figs. 18, 19a) and 40-day

(Figs. 20 and 19b) demineralized samples, discussed above, as well as the demineralization

phase of the remineralized samples (Figs. 24-26, 29-31 and 34-36).

Figure 20. The change in optical absorption (a) and scattering (b) coefficients and thermal

conductivity (c) and diffusivity (d) parameters as a function of time over the 40 day

demineralization period. Layer 1 = surface layer; Layer 2 = lesion body.

0 10 20 30 400

20

40

60

80

100

120

140

Ab

sorp

tio

n C

oe

ffic

ien

t (m

-1)

Treatment Time (days)

Layer 1

Layer 2

0 10 20 30 40

0

25000

50000

75000

100000

125000

150000

Scat

teri

ng

Co

effi

cien

t (m

-1)

Treatment Time (days)

Layer 1

Layer 2

0 10 20 30 40

0.4

0.5

0.6

0.7

0.8

The

rmal

Co

nd

uct

ivit

y (W

/mK

)

Treatment Time (days)

Layer 1

Layer 2

0 10 20 30 40

2.0x10-7

3.0x10-7

4.0x10-7

5.0x10-7

6.0x10-7

7.0x10-7

The

rmal

Dif

fusi

vity

(m

2 /s)

Treatment Time (days)

Layer 1

Layer 2

(a) (b)

(d)(c)

53

Table 9. General trends in the main physical parameters following short and long term

demineralization. The ↑, ↓ and ↔ arrows refer to an increase, decrease or no change,

respectively, in parameters over time.

† A decrease was noted in the 40-day demineralized and high fluoride samples

ffi An increase was observed in the fluoride-free sample

* An increase was observed in the high fluoride sample

¥ Differed depending on initial thickness of the aprismatic layer

4.3 Remineralization Treatment Groups

4.3.1 Microradiographic analysis and visual appearance

Compared to sound enamel, remineralized enamel maintained white-spot enamel appearance

(Fig. 21) induced following demineralization (Fig. 14b). After the 4-week immersion in the low

fluoride and fluoride-free remineralizing solution, there was no difference in the macroscopic

appearance of enamel from after demineralization. A marked change in macroscopic enamel

appearance was evident in samples of the high fluoride group. These changes included enhanced

enamel opacity and chalky-white appearance affecting the entire exposed treatment window (Fig.

21c).

Figure 21. Visual appearance of representative samples from each remineralization treatment

group. (a) Remineralized in the absence of fluoride; (b) remineralized in the presence of low

fluoride; (c) remineralized in the presence of high fluoride levels.

Physical Parameters

Demineralization

0 – 10 days 15 – 40 days

µa1 ↑ ↑

µa2 ↓ ↑

µs1 ↑ ↑

µs2 ↑ ↑

κ1 ↑† ↑

κ2 ↓ ↑

α1 ↓‡ ↑

α2 ↓* ↔

L1 ↑/↓¥ ↑

L2 ↑ ↑

54

Average mineral loss and lesion depths of remineralization and demineralization treatment

groups are presented in Table 10. Analysis of variance of the treatment groups with respect to

mineral loss and lesion depth revealed no significant differences in mean mineral loss (p > 0.05),

and a significant difference in mean lesion depth (p < 0.05). Post hoc statistical analysis (Tukey

test) revealed a significant difference in mean lesion depth between all 3 remineralization groups

relative to the demineralized control (p < 0.05). No significant differences were found between

the 3 remineralization treatment groups with respect to mineral loss or lesion depth.

Table 10. Average mineral loss and lesion depth of remineralization and demineralized

treatment groups. Means with different letters are significantly different at p < 0.05.

4.3.2 Fluoride-free remineralization group

4.3.2.1 Microradiographs and mineral content depth profiles

An exemplary sample from the fluoride-free group revealed a heavily mineralized superficial

enamel layer, overlying the intact surface layer and body of the lesion (Fig. 22). This typical

mineral volume distribution was the most frequently observed occurring in 80% of remineralized

samples. Hypermineralized surface layers, with respect to the intact surface layer and lesion

body, were present at mineral volume approaching sound enamel and higher than the mineral

volume of the subadjacent intact surface layer. In these samples, mineral volume peaks occurred

directly at the enamel surface and in microradiographic images displayed as thin radiopaque

surface layers discernible from underlying mineral layers.

Treatment Group Mean mineral loss (vol%.µm) Mean lesion depth (µm)

No fluoride 1055 ± 257 65 ± 7a

Low fluoride (1 ppm) 1087 ± 452 64 ± 11a

High fluoride (1000 ppm) 932 ± 373 60 ± 15a

Demineralized only 1247 ± 502 90 ± 12b

55

Figure 22. Microradiographic image and mineral volume profile for an exemplary sample from

the fluoride-free treatment group.

4.3.2.2 PTR-LUM frequency response

PTR and LUM amplitude and phase signals for the sample microradiograph shown in Fig. 22 are

presented in Fig. 23. In order to enhance the trends of signal behaviour following

remineralization, amplitude ratios and phase differences with respect to the final

demineralization amplitude and phase signals are presented. Amplitude ratios greater or less than

unity indicate an increase or decrease in amplitude above or below the final demineralization

curve, respectively, across the probed modulation frequency range. Positive and negative phase

differences refer to smaller and larger phase lags, respectively. Following demineralization until

the final remineralization treatment point there was a trend of increasing PTR amplitude across

the entire frequency range and decrease in PTR phase lag, particularly at low modulation

frequencies. The PTR amplitude shifted very slowly during the first 10 days of exposure to the

mineralizing solution, however, following 10 days the curves rapidly and consistently increased

in amplitude until the end of the exposure period. An increase in phase lag occurred at all

treatment points except day 10, where a drastic and transient decrease in phase lag was observed

at high modulation frequencies. Amplitude ratios and phase differences under 830-nm radiation

revealed similar PTR features as noted under 660-nm (Appendix 1; Fig. A.1.2).

LUM amplitude ratios, normalized with respect to the final demineralized curve, revealed

relatively flat frequency dependence. Over the course of both de- and remineralization

treatments, the flat appearance was maintained, whereas vertical shifts in amplitude dominated.

LUM phases exhibited minima in the modulation frequency range 63 - 100 Hz. Large decreases

100 µm

56

in LUM amplitude and phase minima occurred over the first 10 days. A slight increase in

amplitude and phase after 20 days was followed by a reversal and decrease at 28 days.

Figure 23. PTR-LUM amplitude ratios and phases differences with respect to the final

demineralization state for a sample in the fluoride-free treatment group, under 660nm laser

excitation. The corresponding microradiograph and mineral volume profile is shown in Fig. 22. Error bars, when not visible, are of the size of the symbols.

4.3.2.3 Theoretical analysis of fluoride-free remineralized samples

An excellent fit between PTR experimental data and 3-layer theory was found for the fluoride-

free sample (Appendix 2; Fig. A.2.3). The change in optical parameters (absorption and

scattering coefficients), thermophysical parameters (diffusivity and conductivity) and layer

thicknesses as a function of demineralization time (10-day) and subsequent remineralization (4-

week) in the fluoride-free solution is shown in Figs. 24-26. Plots of the additional parameters

over treatment time are given in Appendix 3. Trends in optical and thermal properties over the

1 10 100 10001.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0

Am

plit

ude R

atio (

V/V

0)

Frequency (Hz)1 10 100 1000

0.80

0.84

0.88

0.92

0.96

Remin- 2 Days

Remin- 5 Days

Remin- 10 Days

Remin- 20 Days

Remin- 28 Days

PTR Amplitude LUM Amplitude

Am

plit

ude R

atio (

V/V

0)

Frequency (Hz)

1 10 100 1000

-4

-2

0

2

4

6

8 PTR Phase

Phase D

iffe

rence (-

0)

Frequency (Hz)10 100

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0.1LUM phase

Phase D

iffe

rence (-

0)

Frequency (Hz)

57

10 day demineralization period are consistent with those described in the previous section for

demineralized samples. At the onset of remineralization, a decrease in optical absorption

coefficient of both layers for 10 days was followed by a linear increase in the properties of layer

1 until the end of the 4-week period (Fig. 24A). Optical scattering coefficients continued to rise

within the lesion body and within the surface layer a marked increase in surface scattering was

noted at the 10 day remineralization period (Fig. 24B). This is consistent with the smaller phase

lag at high modulation frequencies and increase in slope of the amplitude ratio of the 10-day

remineralized curve (Fig. 23).

Figure 24. Change in optical absorption (A) and scattering coefficients (B) over treatment time

for a sample in the fluoride-free treatment group. Vertical dashed lines separate demineralization

and remineralization treatments. Layer 1 = surface layer; Layer 2 = lesion body.

At the onset of remineralization, a large decrease in thermal diffusivity (Fig. 25B) of the surface

layer occurred with a small increase in the subsurface layer. Surface layer diffusivity increased

over the remineralization period and saturated after 10-day remineralization. The diffusivity of

the lesion body changed in a similar fashion, decreasing monotonically after the first day of the

10-day remineralization. Thermal conductivities (Fig. 25A) exhibited similar trends to

diffusivities: that of the surface layer also increased with increasing remineralization time,

whereas small increases were only found after 5 days of remineralization.

0 10 20 30 40

0

25000

50000

75000

100000

125000 Demin Remin

Scat

teri

ng

Co

eff

icie

nt

(m-1

)

Treatment Time (days)

Layer 1

Layer 2

(A) (B)

0 10 20 30 40

20

40

60

80

100

120

Demin Remin

Ab

sorp

tio

n C

oef

fici

ent

(m-1

)

Treatment Time (days)

Layer 1

Layer 2

58

Figure 25. Change in thermal conductivity (A) and diffusivity (B) over treatment time for a

sample in the fluoride-free treatment group. Vertical dashed lines separate demineralization and

remineralization treatments. Layer 1 = surface layer; Layer 2 = lesion body.

Changes in layer thicknesses (Fig. 26) were dominant within the first 10 days of

remineralization, where a significant decrease in thickness of the lesion body occurred with a

concomitant increase in thickness of the surface layer. Minimal changes in thickness occurred

after the 10 day remineralization period.

Figure 26. Change in layer thicknesses over treatment time for a sample in the fluoride-free

treatment group. The vertical dashed line separates de- and remineralization treatments. Layer 1

= surface layer; Layer 2 = lesion body.

0 10 20 30 40

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

ReminDemin

Ther

mal

Co

nd

uct

ivit

y (W

/mK

)

Treatment Time (days)

Layer 1

Layer 2

0 10 20 30 40

2.0x10-7

3.0x10-7

4.0x10-7

5.0x10-7

6.0x10-7

7.0x10-7

ReminDemin

Ther

mal

Dif

fusi

vity

(m

2 /s)

Treatment Time (days)

Layer 1

Layer 2

(A) (B)

0 10 20 30 40

0

10

20

30

40

50

60

70

80

90

ReminDemin

Laye

r Th

ickn

ess

(m

)

Treatment Time (days)

Layer 1

Layer 2

59

4.3.3 Low fluoride (1 ppm) remineralization group

4.3.3.1 Microradiographs and mineral content depth profiles

An exemplary sample from the low fluoride group revealed a more discernible approximate 3-

layer geometrical lesion structure, outlining a radiodense intact surface layer overlying the lesion

body and followed by bulk sound enamel (Fig. 27).

Figure 27. Microradiographic image and mineral volume profile for an exemplary sample from

the low fluoride treatment group.

4.3.3.2 PTR-LUM frequency response

PTR-LUM frequency response is shown in Fig. 28. A consistent trend of increasing PTR

amplitude across the entire modulation frequency range and decrease in phase lag at low

frequencies from the final demineralization curve to the final remineralization curve was evident.

However, marked differences were evident at earlier and later mineral solution exposure times.

Large separation appeared between measurements in the first 10 days and subsequent

measurements at later periods. Furthermore, trends of increased slope in PTR amplitude and

phase with a marked approximately linear increase in amplitude from low to high modulation

frequencies were evident at later remineralization times. Significant amplitude depression at the

inception of the exposure period was noted and continued for 10 days. Amplitude ratios and

phase differences under 830-nm radiation revealed a near-monotonic increase in amplitude with

a notable change in slope increasing toward the high modulation frequencies (Appendix 1; Fig.

A.1.3).

LUM amplitude and phase behaviour mirrored changes in PTR where a reversal in direction in

both amplitude and phase occurred for the first 10 days of remineralization. It is also important

100 µm

60

to note that LUM trends are opposite those of PTR, such that higher PTR signal amplitude

correlated with lower LUM signal amplitude and vice versa.

Figure 28. PTR-LUM amplitude ratios and phases differences with respect to the final

demineralization state for a sample in the low fluoride treatment group, under 660nm laser

excitation. The corresponding microradiograph and mineral volume profile is shown in Fig. 27. Error bars, when not visible, are of the size of the symbols.

4.3.3.3 Theoretical analysis of low fluoride remineralized samples

An excellent fit was found between experimental and theoretical data for the final demineralized

PTR curve and all remineralized curves (Appendix 2; Fig. A.2.4). Changes in optothermal

properties during the initial demineralized phase are consistent with the previous description of

demineralized control samples. An increase in absorption coefficient of the lesion body occurred

over the 10-day remineralization period (Fig. 29A) with an increase in the surface layer from day

20 until day 38. A marked decrease in the scattering properties of the lesion body occurred over

1 10 100 1000

0.85

0.90

0.95

1.00

1.05

1.10

1.15

1.20

1.25

Am

plit

ude R

atio (

V/V

0)

Frequency (Hz)1 10 100 1000

0.80

0.84

0.88

0.92

0.96

1.00

1.04

1.08

Remin- 2 Days

Remin- 5 Days

Remin- 10 Days

Remin- 20 Days

Remin- 28 Days

PTR Amplitude LUM Amplitude

Am

plit

ude R

atio (

V/V

0)

Frequency (Hz)

1 10 100 1000

-3

-2

-1

0

1

2

3

4

5 PTR Phase

Phase D

iffe

rence (-

0)

Frequency (Hz)10 100 1000

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2 LUM phaseP

hase D

iffe

rence (-

0)

Frequency (Hz)

61

the first 5 days of remineralization (Fig. 29B). From the 5-day remineralization period onward

scattering properties began to rise and increased above the final demineralized state at the 30-40-

day overall treatment period. Scattering properties of the surface layer were insignificant

compared to the dominant changes which occurred within layer 2.

Figure 29. Change in optical absorption (A) and scattering coefficients (B) over treatment time

for a sample in the low fluoride treatment group. Vertical dashed lines separate demineralization

and remineralization treatments. Layer 1 = surface layer; Layer 2 = lesion body.

At the onset of remineralization, an increase in the thermal properties of the lesion body was

noted over the first 10 days (Fig. 30A, B), which then began to decrease at prolonged treatment

times consistent with the PTR amplitude and phase frequency response (Fig. 28). The

improvement in the thermal conductivity of the lesion body occurred with the generation of a

transient poorer conductivity of the surface layer (Fig. 30A). After 20 and 28 days of

remineralization an increase in the thermal conductivity of the surface layer was evident.

Diffusivities followed a similar pattern; however, properties of the surface layer remained higher

than the subsurface layer and increased from day 5 - 28 (Fig. 30B).

0 10 20 30 40

0

25000

50000

75000

100000

125000

150000

Demin Remin

Scat

teri

ng

Co

effi

cien

t (m

-1)

Treatment Time (days)

Layer 1

Layer 2

(A) (B)

0 10 20 30 400

20

40

60

80

100

120

140

Demin Remin

Ab

sorp

tio

n C

oef

fici

ent

(m-1

)

Treatment Time (days)

Layer 1

Layer 2

62

Figure 30. Change in thermal conductivity (A) and diffusivity (B) over treatment time for the

low fluoride sample. Vertical dashed lines separate de- and remineralization treatments. Layer 1

= surface layer; Layer 2 = lesion body.

A large reduction in the thickness of the lesion body occurred over the first 10 days of

remineralization with almost no change in thickness thereafter (Fig. 31). The large decrease in

thickness of the lesion body occurred with a simultaneous increase in thickness of the surface

layer from day 0 to day 10 of remineralization.

Figure 31. Change in layer thicknesses over treatment time for a sample in the low fluoride

treatment group. The vertical dashed line separates de- and remineralization treatments. Layer 1

= surface layer; Layer 2 = lesion body.

0 10 20 30 40

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

ReminDemin

The

rmal

Co

nd

uct

ivit

y (W

/mK

)

Treatment Time (days)

Layer 1

Layer 2

0 10 20 30 40

2.0x10-7

3.0x10-7

4.0x10-7

5.0x10-7

6.0x10-7

7.0x10-7

ReminDemin

Th

erm

al D

iffu

sivi

ty (

m2 /s

)

Treatment Time (days)

Layer 1

Layer 2

(A) (B)

0 10 20 30 40

0

10

20

30

40

50

60ReminDemin

Laye

r T

hic

kne

ss (

m)

Treatment Time (days)

Layer 1

Layer 2

63

4.3.4 High fluoride (1000 ppm) remineralization group

4.3.4.1 Microradiographs and mineral content depth profiles

An exemplary sample from the high fluoride group showed a hypomineralized layer above the

intact surface layer which reached a maximum mineral volume at a depth below the enamel

surface (≈14 µm) (Fig. 32). Surface hypomineralization was evident in 70% of the high fluoride

group. Poorer distinction between the intact surface layer and the subsurface lesion was due to

reduced subsurface radiolucency.

Figure 32. Microradiographic image and mineral volume profile for an exemplary sample from

the high fluoride treatment group.

4.3.4.2 PTR-LUM frequency response

PTR-LUM frequency responses for a sample from the high fluoride group are presented in Fig.

33. A decrease in low-frequency amplitude up to the 10-day exposure period was evident.

Onward from the 10-day exposure period a substantial increase in PTR amplitude across all

modulation frequencies and decrease in PTR phase lag at low modulation frequencies occurred.

The low frequency PTR phase pattern was accentuated with increasing exposure time: smaller

phase lag and more pronounced curvature of phase maxima. A trend consistent among all

samples remineralized in the presence of high fluoride concentrations was the decrease in PTR

amplitude across the entire modulation frequency range from the 20 day to the 28 day exposure

period. This occurred with a concomitant increase in phase lag at low modulation frequencies.

Nearly identical trends were evident for frequency scans with the 830-nm laser (Appendix 1; Fig.

A.1.4). As noted for the other 2 treatment groups, poor SNR of the 830-nm laser made small

phase changes due to remineralization difficult to discern. LUM amplitude and phase signals did

not exhibit trends consistent with treatment time; however, they reflected changes in PTR

100 µm

64

amplitude at high frequency. Larger PTR amplitude at high frequencies correlated with lower

LUM amplitude and vice versa. Little change in amplitude accompanied a decrease in phase at 2

days of remineralization. Marked reduction in LUM amplitude occurred after 5 and 10 days of

remineralization in both samples. This was followed by a large increase in amplitude and phase

at 20 days of remineralization, which continued to increase at day 28.

Figure 33. PTR-LUM amplitude ratios and phase differences with respect to the final

demineralization state for a sample in the high fluoride treatment group, under 660nm laser

excitation. The corresponding microradiograph and mineral volume profile is shown in Fig. 32.

Error bars, when not visible, are of the size of the symbols.

4.3.4.3 Theoretical analysis of high-fluoride remineralized samples

Optical and thermal properties and thicknesses of the high fluoride sample are shown in Figs. 34-

37. The depth profiles were constructed from the fitting of 3-layer theory to experimental PTR

1 10 100 1000

1.0

1.2

1.4

1.6

Am

plit

ude R

atio (

V/V

o)

Frequency (Hz)1 10 100 1000

0.84

0.88

0.92

0.96

1.00PTR Amplitude LUM Amplitude

Am

plit

ude R

atio (

V/V

o)

Frequency (Hz)

1 10 100 1000

-4

-2

0

2

4

6

8

Remin- 2 Days

Remin- 5 Days

Remin- 10 Days

Remin- 20 Days

Remin- 28 Days

PTR Phase

Phase D

iffe

rence ( -

0)

Frequency (Hz)10 100 1000

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

LUM phase

Phase D

iffe

rence ( -

0)

Frequency (Hz)

65

curves, which showed an excellent fit with a small residual (Appendix 2; Fig. A.2.5). Optical

properties (Fig. 34) during the demineralized phase followed trends identified for the 10-day

treated samples of the demineralized control group; however a different thermophysical profile

was evident (Fig. 35). It is noteworthy to point out a marked increase in the scattering coefficient

of layer 1 after 5 days of demineralization (Fig. 34B). A large decrease in conductivity (Fig.

35A) of both layers occurred at 5 days of demineralization while smaller changes in diffusivity

occurred (Fig. 35B).

An increase in the scattering coefficient of the lesion body after 2 days of remineralization

rapidly declined at prolonged exposure times. A slight reversal in the scattering properties led to

an increase at the 28-day remineralization period. Changes in the scattering properties of the

surface layer were small compared to the dominant changes in the lesion body.

Figure 34. Change in optical absorption (A) and scattering coefficients (B) over treatment time

for a sample in the high fluoride treatment group. Vertical dashed lines separate demineralization

and remineralization treatments. Layer 1 = surface layer; Layer 2 = lesion body.

Remineralization enhanced the thermophysical properties of both layers over the 10-day

remineralization period. At longer layer exposure periods to the fluoride solution, a marked

decrease in both thermal conductivity (Fig. 35A) and thermal diffusivity (Fig. 35B) was

observed.

0 10 20 30 40

20

30

40

50

60

70

80

90

100

110

120

Demin Remin

Ab

sorp

tio

n C

oe

ffic

ien

t (m

-1)

Treatment Time (days)

Layer 1

Layer 2

0 10 20 30 40

0

20000

40000

60000

80000

100000

120000

140000

160000

Demin Remin

Scat

teri

ng

Co

eff

icie

nt

(m-1

)

Treatment Time (days)

Layer 1

Layer 2

(B)(A)

66

Figure 35. Change in thermal conductivity (A) and diffusivity (B) over treatment time for a

sample in the high fluoride treatment group. Vertical dashed lines separate de- and

remineralization treatments. Layer 1 = surface layer; Layer 2 = lesion body.

A significant decrease in thickness occurred within the lesion body over the 10-day

remineralization period, following a steep increase during the early demineralization period (Fig.

36). Little-to-no change was observed in the thickness of the surface layer over the 4 week

remineralization period.

Figure 36. Change in layer thicknesses over treatment time for a sample in the high fluoride

treatment group. The vertical dashed line separates de- and remineralization treatments. Layer 1

= surface layer; Layer 2 = lesion body.

A summary of the typical trends in the core physical parameters following demineralization and

remineralization are presented in Table 11. The trends during demineralization are the same as

those outlined in Table 9. The trends evaluated in Table 11 are compiled from Figs. 24-26, 29-31

0 10 20 30 40

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

ReminDeminTh

erm

al C

on

du

ctiv

ity

(W/m

K)

Treatment Time (days)

Layer 1

Layer 2

0 10 20 30 40

2.0x10-7

3.0x10-7

4.0x10-7

5.0x10-7

6.0x10-7

7.0x10-7

ReminDemin

The

rmal

Dif

fusi

vity

(m

2 /s)

Treatment Time (days)

Layer 1

Layer 2

(B)(A)

0 10 20 30 40

0

10

20

30

40

50

60

70

ReminDemin

Laye

r Th

ickn

ess

(

m)

Treatment Time (days)

Layer 1

Layer 2

67

and 34-36 and separate short-term trends (0 – 10 days) from long-term trends (20 – 28 days)

during remineralization.

Table 11. General trends in the main physical parameters following demineralization and short

vs. long term remineralization. The arrows indicate trends where ↑, ↓ and ↔, refer to an increase,

decrease or no change, respectively, in parameters over time.

† A decrease was noted in the 40-day demineralized and high fluoride samples

ffi An increase was observed in the fluoride-free sample

* An increase was observed in the high fluoride sample

¥ Differed depending on initial thickness of the aprismatic layer

5 Discussion

A common limitation in in vitro cariology research is that a direct measure of mineral content

during de- and remineralization evaluation is destructive in nature. Furthermore, frequently used

substrates for de- and remineralization experiments include thin, polished enamel sections rather

than whole teeth. It has been repeatedly demonstrated that abraded enamel samples demineralize

and remineralize at different rates and extent than enamel that has its natural surface intact (Xue

et al. 2009). As a result, studies implementing polished, ground or abraded enamel sections cause

a significant removal of surface structural features (i.e. aprismatic enamel), precluding the

identification of surface enamel influences and diverging farther from in vivo relevancy.

5.1 PTR-LUM signals and multiparameter fits of sound enamel

Since the natural enamel surface modulates the chemical reactions between the internal sound

enamel structure and external oral environment, proper characterization of its properties are

Physical Parameters

Demineralized Remineralized Remineralized Remineralized

No fluoride Low fluoride High fluoride

0 – 10 days 0 – 10 days

20 – 28 days

0 – 10 days

20 – 28 days

0 – 10 days

20 – 28 days

µa1 ↑ ↓ ↑ ↑ ↑ ↔ ↑

µa2 ↓ ↓ ↑ ↑ ↓ ↑ ↑

µs1 ↑ ↑ ↓ ↓ ↑ ↑ ↓

µs2 ↑ ↑ ↑ ↓ ↑ ↓ ↑

κ1 ↑† ↑ ↑ ↓ ↑ ↑ ↓

κ2 ↓ ↑ ↔ ↑ ↓ ↑ ↓

α1 ↓‡ ↓ ↔ ↓ ↑ ↑ ↓

α2 ↓* ↓ ↔ ↑ ↓ ↑ ↓

L1 ↓¥ ↑ ↔ ↑ ↔ ↔ ↔

L2 ↑ ↓ ↔ ↓ ↔ ↓ ↔

68

essential. To date, there have been few reports on the surface characterization of aprismatic

enamel, mainly a result of its removal in in vitro studies coupled with the fact that its

infinitesimal thickness lies at the lower detection limit of current evaluation techniques and is

often presented as continuous and indistinct from the underlying bulk enamel. Initial attempts to

fit experimental PTR amplitude and phase to diffuse photon density and thermal wave theory

based on 2 effective layers where L1 and L2 were enamel and dentin, respectively, yielded poor

quality fits. However, recently, the introduction of a layer at the enamel surface with optothermal

properties different from bulk enamel, termed the aprismatic layer, resulted in a good fit of

experimental data to theory (Matvienko et al. 2009b). In the present study, the 2-layer

approximation of sound enamel, where layer 1 is the aprismatic layer and layer 2 is semi-infinite

sound enamel was implemented (Fig. 11). Although aprismatic enamel is more prevalent in

unerupted and deciduous dentition (primarily molars), it has also been observed in about 70% of

permanent human molars at varying thickness depending on the tooth surface (Gwinnett 1967),

and therefore its presence was considered to play an integral role at the superficial aspect of

sound enamel. Furthermore, evidence that the surface layer indeed represented a layer of

aprismatic enamel could not be discerned from microradiographic analysis (Fig. 15). Earlier

studies documented that the outermost layers of enamel were occasionally hypermineralized and

appeared as radiodense zones on microradiographs (Gwinnett 1967; Darling and Crabb 1956).

The described structurally dense crystallite packing and reduced pore volume of aprismatic

layers (Gwinnett 1967) are in contrast to the surface hypomineralization observed in the

microradiographs of sound teeth in the present study (Fig. 15). However, it has also been stated

that to date there is no evidence to suggest that the aprismatic layer is hypo- or hyper-mineralized

compared to underlying enamel (Ripa et al. 1966; Gwinnett 1967). The characterization of a thin

surface layer in the theoretical representation of sound enamel may likely be influenced by a

combination of factors, including: the presence of a residual aprismatic layer, surface mineral

loss due to the storage conditions of the extracted samples prior to experimentation (distilled

water at 40C), abrasion of the enamel surface during the tooth‘s lifetime in the oral cavity and

lastly the higher fluoride concentrations that may form a distinct mineral phase (F-OHAp) at the

outermost enamel (Weatherell et al. 1974). All of the aforementioned sources may contribute to

the generation of a surface layer with variable optothermal properties. For the purposes of the

69

present investigation, all of these sources were classified under the general term ―aprismatic‖,

even though the surface layer is not likely to be completely devoid of prisms.

Analysis of the optothermal parameters derived from the theoretical fittings of PTR amplitude

and phase signals of untreated teeth revealed highly variable opto-thermophysical properties of

layer 1 (aprismatic enamel) whereas the properties of layer 2 (sound prismatic enamel) fell

within a narrow range (Table 8). As expected, the values derived for sound enamel were

consistent with the values found in earlier literature (Tables 1 and 2), since the literature values

were used as guidelines to define the initial limits of the fitting program. The computational

program optimally selected parameter values between the literature-defined limits without

converging to the upper/lower parameter ranges in order to yield the smallest residual between

experimental data and theory. In terms of the optical properties, the diffuse prism-packing and

the presence of amorphous mineral deposits within the aprismatic surface layer has been

suggested to act as optical gatherers (Gwinnett 1967; Odor et al 1996). A higher PTR-derived

mean optical absorption coefficient in the aprismatic layer (65 m-1

) compared to sound enamel

(44 m-1

) supports this earlier observation (Table 8). The largest deviation in optothermal

properties in sound enamel was observed in the thermal properties of the aprismatic vs. prismatic

enamel (Table 8). A slightly higher thermal diffusivity and poorer thermal conductivity of the

aprismatic layer compared to the underlying enamel, may suggest a much lower density of this

layer as diffusivity due to the relationship between density and diffusivity (See equation 1). This

is further supported by the evidence of surface hypomineralization in mineral content depth

profiles (Fig. 15). The presence of surface discontinuities, such as the aprismatic layer, resulted

in poorer thermal properties, thereby generating a thermally impeding layer at the most

superficial aspect of sound enamel. This would effectively reduce thermal diffusion lengths as

near-surface thermal-wave confinement dominates. From PTR scans of untreated teeth, phase

frequency responses were near-linear at lower modulation frequencies, however exhibited phase

peaks in the high frequency range. The observation of phase maxima at higher modulation

frequencies is consistent with the generation of a thermal-wave interference pattern occurring

closer to the anatomical surface. Given the frequency at which phase maxima appear, above 100

Hz, and the mean thermal diffusivity values of sound enamel from the fitted data (4.41 x 10-7

m2/s) (Table 8), the corresponding mean thermal diffusion length is approximately µ (100 Hz) ≈

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37.5 µm. This thermal diffusion length corresponding to the phase maxima at 100 Hz, the lowest

frequency where maxima appeared in sound enamel was similar to the largest thickness of the

aprismatic layer determined from TMR analysis (44 µm). The theoretically derived thickness of

the aprismatic layer was on average ≈13 µm, with a maximum thickness of ≈22 µm. These

thickness values are in line with previous investigations by Ripa (1966) and Gwinnett (1967)

who observed average surface layer zones of 30 µm and 20 µm, respectively. Whittaker (1982)

found that the most frequently observed (42 - 53%) width of the aprismatic layer in lingual

enamel of permanent molars and 3rd

molars was between 16 – 45 μm.

The overall characterization of the outermost enamel surface layer is vital as all chemical attacks

on enamel, be it caries or erosion, are modulated by surface enamel properties. This layer may be

an important determinant in the overall caries susceptibility of enamel; its incidence has been

previously related to lower caries rates (Jackson 1971). As the occurrence of thick aprismatic

surface layers was low, a causal relationship between aprismatic layer thickness and the depth of

the subsequently demineralized lesion could not be established. Analysis of sound enamel in this

study illustrated the capability of PTR-LUM to non-destructively evaluate and quantify the

properties of untreated intact enamel surfaces. This would be invaluable in dental research in

terms of selecting more uniform enamel substrates for in vitro or in vivo demineralization and

remineralization studies. This is supported by the fact that the properties of the untreated sample

can have a marked response on subsequent de- and remineralization (Groeneveld et al. 1975;

Brudevold et al. 1968; Xue et al. 2009). Extrapolation to clinical environments may allow for the

identification of caries susceptible sites on enamel and further, may be implicated in time-

dependent enamel etching and bonding techniques.

5.2 PTR-LUM signals during short and long-term demineralization

At the first exposure of the sound enamel to the demineralizing solution, the 2-layer theoretical

approximation was no longer valid, and instead a 3-layer theoretical approximation was

considered, where layer 1, 2 and 3 were the intact surface layer, lesion body and sound enamel,

respectively (Fig. 12). The intact surface layer may be a combination of aprismatic and

remineralized enamel; however, since the first PTR measurement occurred after 5 days of

demineralization it is likely that the latter dominated. During demineralization a consistent trend

71

of increasing PTR amplitude with a concomitant decrease in PTR phase lag and a shift of the

phase peaks to lower frequencies were observed (Figs. 16 and 17). These trends suggest the

formation of a depth-wise growing subsurface lesion as documented elsewhere (Jeon et al. 2008;

Jeon et al. 2004a; Nicolaides et al. 2002). Changes in PTR phase with demineralization are

attributed to thermal-wave interference patterns within the demineralized lesion, which increases

in thickness during the demineralization period.

5.2.1 Multiparameter fits of PTR signals during demineralization

PTR amplitude and phase trends can be explained based on the generated set of optical and

thermal properties of each effective layer (Figs. 18 - 20). Prior to the discussion of the trends in

opto-thermophysical properties during demineralization it is important to highlight the

uniqueness of the fitted parameters, which is examined in detail in Appendix 4. The convergence

of the fitted parameters, in particular thicknesses, to similar values under different parameter

ranges (Appendix 4; Table A.4.2) illustrates the robustness of the computational algorithm and

the reliability of the derived values from the best fits of experimental data. Opto-thermophysical

properties of demineralized samples were generated from the theoretical fitting program by first

fitting the final demineralized PTR amplitude and phase curve, using thicknesses from the final

TMR as guidelines (Fig. 13). Given the PTR amplitude and phase curve fittings and parameters

extracted from the untreated state and from the final demineralized state, the thicknesses from

the 2 treatment end points were used to fit frequency scan data from intermediate treatment

points. Optical absorption coefficients for layer 1 increased with demineralization time, while no

trend was evident in the absorption properties of the lesion body (Figs. 18a and 20a). Larger

absorption coefficients result in a stronger thermal wave field and consequently larger amplitude.

The higher spatial rate of photon absorption within layer 1 results in the confinement of the

subsurface extent of the thermal wave to a narrower region causing a higher amplitude and

smaller phase lag (Matvienko et al. 2009b). An earlier study that determined optical properties

from enamel slabs revealed that there was no evidence of an increase or decrease in optical

absorption coefficients between sound and carious enamel, however large errors (>40%) in the

calculated absorption coefficients were observed (Spitzer and ten Bosch 1977). Higher scattering

coefficients of the developing lesion (layer 1 and 2) are also consistent with the aforementioned

PTR trends (Figs. 18b and 20b). Upon demineralization, changes in the scattering coefficient

72

were more dominant than changes in the absorption coefficient, as has been documented

previously (Spitzer and ten Bosch 1977). This was caused by crystalline disintegration of the

enamel structure and the generation of small pores which can act as scattering centers (Darling et

al. 2006; Angmar-Månsson and ten Bosch 1987; Zijp 2001). Higher scatter of the diffuse-photon

density field results in shorter optical path lengths within enamel (Angmar-Månsson and ten

Bosch 1987) which photothermally is tantamount to a higher absorption coefficient and increases

the generated PTR signal. The previously documented higher reflectance and poorer

transmission properties of carious lesions would likely contribute to the localization of the

optical field to a narrow region, lessening the influence of the underlying layers (Ko et al. 2000;

Spitzer and ten Bosch 1977). As photons are localized to a narrower surface region, a higher

probability for absorption and non-radiative conversion processes would confine the thermal

wave centroid closer to the enamel surface (Matvienko et al. 2009a; Mandelis and Feng 2002).

The scattering properties of both layer 1 (surface layer) and layer 2 (lesion body) increased

substantially from the start of demineralization, with greater scattering contribution from the

demineralized lesion body near the end of the treatment period (Figs. 18b and 20b). Considering

only the first 20 days, a rapid increase in the scattering coefficient of the lesion body from day 0

– 10 followed a more gradual change from 10-20 days (Fig. 20b). Replacement of the

demineralizing medium with a fresh aliquot after 20 days most likely dissipated the chemical

gradients in the gel surrounding the enamel accelerating the demineralization rate until near-

saturation conditions were restored. This may explain the linear increase in scattering coefficient

of the lesion body from the 20 – 40-day period, as well as the concomitant increase in lesion

depth over the same period (Fig. 19b). As incipient lesions typically generate an increasingly

inhomogeneous medium, a higher scattering coefficient was expected relative to sound enamel.

Substantial increases in the scattering coefficient of demineralized enamel relative to sound

enamel have been documented. Darling et al. (2006) found an increase in the scattering

coefficient by 1 or 2 orders of magnitude over the scattering coefficient of sound enamel. Spitzer

and ten Bosch (1977) found a scattering coefficient of white spot lesions to be 5 -10 times higher

than sound enamel. Higher scattering within the lesion body may occur since this zone occupies

the largest volume within a carious lesion, decreasing in mineral volume from 87 vol% at the

sound enamel level to ≈60 vol% in the subsurface minimum. Subsurface demineralization is

73

characterized by the enlargement of the micropores through central core dissolution of crystals

(Palamara et al. 1986). The enlargement of the micropores and the spaces at the prism

boundaries make the tissue more penetrable to the influx of acids from the demineralizing

medium and the out-diffusion of dissolved minerals from the dissolution reaction. The enhanced

scattering properties of the intact surface layer may be due to the composite nature of this layer

during demineralization. The outer surface layer maintains a level of porosity greater than sound

enamel and less than the lesion body (Figs. 16 and 17). Furthermore, the intact surface layer

most likely acquired minerals along its inner surface, deposited from the out-diffused flux at the

advancing lesion front, as well as outer surface, from mineral deposition from the demineralizing

solution at later treatment times as the buildup of mineral ions in solution increased and the

driving force (degree of saturation) for demineralization was reduced. Miake et al. (2003) and

Tohda et al. (1990) showed that demineralized surface layers contained a large number of

irregularly shaped crystals of various sizes. The presence of unstructured crystals in the surface

layer would augment the scattering properties of layer 1 by creating additional crystal grain

boundaries, as seen in Fig. 20B.

The generation of layers with poorer thermal properties was supported by theoretical analysis

which consistently showed a decrease in thermal conductivity and diffusivity of the lesion body

(layer 2) (Figs. 18c, d and 20c, d). The creation of small micro-channels within the

demineralized lesion may generate an impedance to heat propagation resulting in a poorer

thermal conductivity. A reduction in the thermal conductivity would result in a corresponding

reduction in thermal diffusivity based on equation 1. The poorer thermal diffusivity of the lesion

body may impede back-propagation of thermal wave contributions from much deeper regions

from reaching the enamel surface and as a result confine the region of thermal wave field within

the growing demineralized layer. Investigations on the extraction of thermal properties, namely

conductivity and diffusivity, from carious and sound enamel are scarce. A reduction in the

thermal properties in artificially demineralized lesions relative to sound enamel was observed by

El-Brolossy et al. (2008) using photoacoustic spectroscopy; however, the extent of reduction in

conductivity (0.72 W/mK) and diffusivity (3.81x10-7

m2/s) values for demineralized enamel were

far less than those observed in the present study (Figs. 18c, d and 20c, d). Intuitively, it might be

expected that thermal diffusivity would increase with demineralization due to its inverse relation

74

to density (equation 1), which decreases within a lesion. However, the increase in lesion porosity

results in filling of the enamel pores with a combination of air and water, both of which have a

poorer thermal conductivity than sound enamel (≈0.87 Wm-1

K-1

), 0.026 and 0.598 Wm-1

K-1

,

respectively, as well as a higher specific heat capacity (Almond and Patel 1996; Vargaftik et al.

1994). For comparative purposes, dentin, which has intrinsically higher porosity and mineral

volume occupied by water, conductivity (0.577 - 0.623 Wm-1

K-1

) and diffusivity (1.87 - 2.6 x10-7

m2s

-1) values are much lower than enamel (Brown et al. 1970; Braden 1964). This indicates that

the balance between the ratio of thermal conductivity to the product of the density and heat

capacity will ultimately determine the outcome of the thermal diffusivity, as well as the fact that

residual water within the enamel pores may have a significant influence on thermal diffusion

properties of enamel.

Contrasting processes were resolved in the thermal profiles for the surface layer which may be

related to the dynamic dissolution – reprecipitation processes during lesion formation. A rapid

decrease in thermal diffusivity and conductivity of layer 1 for the first 15 days of

demineralization was followed by an increase and stabilization of values (Fig. 20c, d). Initial

exposure of enamel to the demineralizing medium likely results in superficial mineral loss of the

most acid soluble mineral phases. As a result, changes in surface enamel structure would have a

significant impact on the optical and thermal energy generation and propagation. The decreasing

thermal properties of the surface layer may be related to the superficial removal of mineral

phases which may include the ―priming‖ of the enamel surface (Moreno and Zahradnik 1974)

and/or etching of the aprismatic layer. A decrease in thickness of layer 1 in the 10-day

demineralized sample may support the breakdown of the aprismatic layer toward the formation

of the intact surface layer with the concomitant progression of the lesion body inwards (Figs.

19a, 26 and 36). The initial dissolution of enamel has been shown elsewhere (Groenhuis et al.

1980), where a slightly larger surface roughness was induced over a 7 days acid exposure period.

Other studies have found surface erosion within the first 120 – 245 hrs of demineralization

followed by a period of substantial subsurface demineralization (Anderson and Elliott 1992;

Anderson et al. 1998; Zhang et al. 2000a). An increase in roughness would increase the

photothermal signal due to the larger surface area to volume ratio yielding a higher probability

for absorption events and higher thermal wave fields due to confinement at the rough spots. As

75

the thermal properties of the surface layer became poorer for the first 15 days, there would be

effective confinement of optical – thermal energy conversion reactions within this thermally

insulating surface layer, preventing contributions from deeper thermal wave sources (Fig. 20c,

d). After 15 days, the properties increased which may be the result of the well-defined, built up,

intact surface layer overlying the lesion body. The improved thermal properties of layer 1 may

facilitate thermal energy propagation and enhance the interference between forward and L2

interface-interacted (back-propagating) thermal waves. A similar trend was observed in the

optical reflection coefficient between the first 15 days and latter 25 days, where the increase in

the latter 25 days may be the result of optical reflection within the well-defined layers of the

built-up surface layer and lesion body (Appendix 3; Fig. A.3.2c). An increase in optical

reflectivity during demineralization was observed by Baumgartner et al. (2000) using the PS-

OCT system and Ko et al. (2000) with a CCD camera and image-processing software. Surface

dissolution may dominate earlier demineralization times, generating poorer thermal properties in

the surface layer; whereas at later demineralization times the enhancement of the thermal

properties may indicate mineral reprecipitation to restore surface enamel crystallinity. This

reaction mechanism is further supported by the changes in thickness of the intact surface layer

(layer 1) (Fig. 19b-inset), which paralleled the change in thermal properties. Little change in the

thickness of layer 1 was evident for the first 15 days, whereas substantial mineral gains were

found thereafter. Growth of the intact surface layer over time was also observed by Gray and

Francis (1963), Groeneveld et al. (1975) and Gao et al. (1993). This is in contrast to Featherstone

et al. (1978) who observed that after 5-days of demineralization the surface layer formed and its

thickness remained relatively constant thereafter. The stabilized parameters of layer 2 after a

period of time may be explained based on the fact that once the lesion front has passed a certain

depth only minor changes in the mineral volume of the lesion body follow. Thus, the minimum

mineral volume of the lesion body will remain about constant and rather the lesion body acts as a

transport medium for the diffusion of ions to and from the advancing from of the lesion (Arends

et al. 1997). Slight improvements in the thermal properties from the 15-day period onward (Figs.

20c, d) may be attributed to mineral deposition throughout the depth of the lesion as dissolved

mineral ions are transported from the advancing front toward the enamel surface and/or a result

of errors in the theoretical extraction of thermal properties (See Appendix 4).

76

The overall trends in the core physical parameters following short and long-term

demineralization are displayed in Table 9. Of particular note from Table 9 is the fact that the

thickness of the surface layer did not consistently change over the demineralization period.

However, when large aprismatic layers were calculated in the untreated state, the thickness of the

surface layer decreased over time (Fig. 19a). The opposite was found in the case of smaller

aprismatic layers (Fig. 31). In the case of intermediate aprismatic layers, there appeared to be an

initial dissolution, evident in the decrease in surface layer thickness after 5 days, followed by

reprecipitation, evident in the increase in surface layer thickness after 10 days (Fig. 36). Small

deviations from the typical trends, indicated by the symbols in Table 9, may be attributed to

inter-sample biological variability reflected in the different rates and extent of lesion

development. For example, as noted above for the 40-day demineralized sample, the thermal

diffusivity of the surface layer (layer 1) exhibited a two- stage behaviour, where a decrease was

observed following the 10-day demineralization and an increase occurred at later periods, from

day 20 – 40 (Fig. 20d, Table 9). In the fluoride-free sample (Fig. 25B) an increase in the thermal

diffusivity of the surface layer was observed at day 10 of the demineralization phase and may

suggest a more rapid formation and enhanced crystallinity of the surface layer compared to the

40-day demineralized sample. Furthermore, in the high fluoride sample, non-monotonic changes

in thermal properties were observed during demineralization (Fig. 35). The non-monotonicity of

the trends in the physical properties of the high fluoride sample, that cannot be determined from

Table 9, may be related to the deviation of the lesion (Fig. 32) from the assumed 3-layer

geometrical structure due to poorer differentiation between surface and subsurface layers. This

may be explained by the fact that the present study employs a relatively crude 3-layer physical

model representing reality when in fact the lesion is often more complex. Both of the above-

mentioned facts point toward the power of the algorithm used, where the derived opto-

thermophysical parameters change as a function of the lesion structure and not the computational

algorithm.

The change in thermal properties (Fig. 20c, d) and layer thickness (Fig. 19b) paralleled trends in

the PTR amplitude and phase frequency response (Fig. 17). Phase maxima for the first 10 days of

demineralization exhibited a downward shift toward the mid-frequency range with small changes

at higher modulation frequencies. The shifting phase peak toward lower modulation frequencies

77

is indicative of a thermal wave interference pattern forming as a result of the growing subsurface

lesion. As the subsurface lesion increased in thickness, the distance over which the interference

pattern occurred broadened. In the theoretical analysis of the 40-day demineralized sample, no

changes were observed in the thickness of layer 1 for the first 15 days, whereas the lesion body

continued to grow deeper (Fig. 19b). From the 15-day period onward, the emergence of a second

phase peak at higher modulation frequencies (> 100 Hz) (Fig. 17) was concomitant with a large

increase in the derived thickness for layer 1, which reached a maximum thickness of ≈19 µm at

the 40-day demineralization period (Fig 16b - inset). The phase peak at higher modulation

frequencies may indicate a second interference pattern generated by the thickening intact surface

layer. The absence of the aforementioned phase peaks in the 10-day demineralized samples was

most likely due to the smaller surface layer thicknesses (Fig. 16).

Theoretical analysis of PTR amplitude and phase curves allows for the non-destructive

evaluation of mineralization kinetics. Changes in lesion thickness over time for 2 demineralized

samples present different trends as a function of treatment time. From the 10-day demineralized

sample (Fig. 19a) a near-linear relationship between lesion width (thickness of layer 2) and the

demineralization period was evident. A linear relationship between lesion depth and

demineralization time would infer that the rate-controlling process during demineralization is the

reaction at the crystallite level. This means that the dissolution process at the advancing front of

the lesion is slow relative to the diffusion of acid species and mineral ions into and out of the

lesion. Several studies have reported a linear relationship between lesion depth and time

(Anderson et al. 2004; Gao et al. 1993; Arends et al. 1997). When a demineralization gel was

used, a linear relationship between lesion depth and time was observed and attributed to an

inhibitor - controlled dissolution process at the crystallite level (Arends et al. 1997). In the

present acidified gel system, the inhibitor controlled dissolution would be ascribed to the

crystallite adsorption of HEC macromolecules. In the 40-day demineralized sample, a non-linear

rate of lesion growth with time was observed (Fig. 19B). This relationship suggests diffusion-

limited rate of enamel demineralization. Enamel demineralization as a diffusion-controlled

process has been proposed by several earlier studies (Gray 1962; Featherstone 1983; Higuchi et

al. 1965; Wu et al. 1976; Poole et al. 1981; Wong et al. 1987; ten Cate and Arends 1980;

Featherstone et al. 1979; Featherstone and Mellberg 1981). Furthermore, lesion depth varying

78

with the cube root of demineralization time has also been proposed (Groeneveld and Arends

1975; Featherstone et al. 1979), and indicated that diffusive transport of acids and/or dissolved

mineral ions throughout the depth of the lesion to and from the advancing lesion front is the rate

controlling processes. The variance in lesion progression between the 2 samples further

illustrates that the demineralization process is not merely one-dimensional, as changes in

structural gradients, chemical driving forces and porosity, among other factors, complicate the

process and significantly affect the rate of lesion development. A non-linear rate of lesion

progression with time may have been expected due to the mechanism of demineralization in the

present acidified gel system. Gellation of the demineralizing medium generated stagnation

conditions which crudely mimics in vivo dental plaque conditions, in places such as the bottom

of occlusal fissures, gingival margins or approximal sites. The maintenance of ‗sink‘ conditions

within the demineralizing medium means that rapid initial enamel dissolution to remove soluble

mineral phases results in a decrease in the solubility rate with time due to the accumulation of

reaction products and the lower driving force for demineralization (Gray 1962). In the present

study, the entire enamel surface measured was left exposed while other tooth surfaces were

coated in an acid-resistant varnish. As relatively large windows were used in the present study,

mineral concentration at the enamel – gel interface will be much larger than the corresponding

concentrations expected for smaller treatment windows and as a result the rate of lesion

progression will decrease over time (Ruben et al. 1999). Given the above-mentioned mechanism

of demineralization in the acidified gel, the linear relationship in the 10-day demineralized

samples may be influenced by inter- and intra-sample variability due to structural and chemical

gradients, particularly with respect to the utilization of natural enamel surfaces in addition to

error in the derivation of layer thickness for the intermediate demineralization periods.

Determining the lesion depth of the intermediate demineralization times was important for the

longitudinal monitoring of lesion progression and identifying layer thicknesses as destructive

TMR data was unavailable. Calculated mean lesion depth for intermediate demineralized curves

(5 days) was 56.7 ± 18.8 µm, which was within the range of lesion depths from other studies

implementing the same or similar demineralizing system. Boyle et al. (1998) found a mean

lesion depth after 7 days of ≈48 µm, whereas a 7-day immersion in a 0.05 mM lactic acid gel

produced a 38 µm lesion in a study by Issa et al. (2003). ten Cate and Arends (1980) using the

79

same demineralizing solution as the present study found lesion bodies ranging from 15 – 60 µm

with surface layers approximately 15 µm thick after a 4-day treatment period.

5.2.2 LUM signal generation during demineralization

As a complementary signal channel, modulated LUM, which monitors optical radiative

processes, produced consistent trends with treatment time. LUM amplitude decreased

monotonically and phase decreased at the frequency of phase minima (≈89 Hz) with

demineralization time (Figs. 16 and 17). These trends and the poorer contrast between sound and

demineralized enamel are consistent with earlier reports of modulated LUM behaviour to

artificial demineralized lesions (Jeon et al. 2008; Jeon et al. 2004a). The reduction in LUM with

demineralization can fundamentally be explained based on light scattering and absorption

properties of sound relative to demineralized enamel. Lower scattering properties of sound

enamel result in longer photon path lengths and a higher probability of photon absorption and

fluorescence emission from the entire enamel volume, DEJ and/or dentin (Angmar-Månsson and

ten Bosch 1987; Mujat et al. 2003). Alteration of the scattering coefficient in demineralized

enamel may have 2 effects on the level of fluorescence detected. Both scattering of the excitation

light before reaching a fluorophore and/or multiple scattering of the converted fluorescent light

within the tooth before exiting and being collected by the detector, will result in a lower overall

fluorescence collection from demineralized lesions (Girkin et al. 2000). From the onset of

demineralization, internal reflection sites are created as the enamel crystalline structure is broken

down which culminates in the higher optical scattering coefficients relative to sound enamel, as

demonstrated earlier. The higher scattering properties reduce photon path lengths causing a

proportional reduction in the total light path before it emerges at the enamel surface (Angmar-

Månsson and ten Bosch 1987). Borsboom and ten Bosch (1983) found the reduction in the mean

photon path length was about 5 times smaller in carious enamel. Assuming that enamel is not the

only source of fluorescence, the intense scattering properties of demineralized enamel can also

act as a barrier preventing incident photons from interacting with chromophores that lie deeper

toward the DEJ and in dentin (Mujat et al. 2003). These aforementioned mechanisms have been

proposed as explanations for the observed fluorescence loss using the QLF device. Additional

explanations for the loss of autofluorescent properties have been attributed to the loss of

chromophores during the demineralization process and the quenching of fluorescence by a

80

change in the molecular environment of the chromophores (Angmar-Månsson and ten Bosch

2001; Hafstrom-Bjorkman et al. 1992). Stable and high SNR normalized LUM phase curves

exhibited minima in the mid-frequency range characteristic of optical relaxation times

determined for enamel (Nicolaides et al. 2000). In a fluorophore LUM emission rate dynamic

model developed by Nicolaides et al. (2000), LUM emission was assumed to occur through

molecular or electronic radiative processes. From the model, optical relaxation lifetimes were

extracted, the longer of which (on the ms scale) was associated with the phase minimum at ≈30 –

200 Hz, and insensitive to the overall defect state of the tooth. Further insensitivity to the

treatment process was observed in the present study outside the frequency range of phase

minimum, i.e. <30 Hz and >200 Hz. If chromophore lifetimes were altered with demineralization

a shift in the LUM phase extrema to different frequencies would most likely be observed. This

was not the case in the present study, but rather phase minima decreased monotonically. The

decrease at full-width-at-half-maximum may be indicative of the smaller number of excited

chromophores, a result of the intense scattering properties and acid-induced apatite crystal

collapse yielding a reduced radiative conversion processes and lower signal magnitude. This is

evident in the monotonic decreases in LUM amplitude as a function of demineralization time.

Although the exact source of fluorescence has not been identified, it is most probable the

fluorescent properties are derived from both the organic components, such as protein

chromophores, as well as the inorganic mineral components of apatite (Spitzer and ten Bosch

1976). The intense fluorescent properties of dentin have also been proposed to be the result of

multi-source organic and inorganic constituents (Armstrong 1963). This may factor into the

fluorescent properties of enamel as described above, since optical path lengths are much larger in

sound teeth. In contrast to the lower LUM amplitude and phase minima in demineralized vs.

sound enamel and the similar fluorescence intensity reduction described by QLF analyses, the

DIAGNOdentTM

device has demonstrated that carious tissue emitted much stronger fluorescence

intensity relative to sound tissue, at a similar excitation wavelength (λ = 655 nm) as the present

study, increasing by more than one order of magnitude (Hibst and Gall 1998). The source of this

fluorescence has been related to porphyrins derived from bacterial metabolism, which occur at

later stages in caries development where bacterial infiltration and accumulation occur in the

dentin. Moreover, the poor sensitivity for lesions confined to enamel (Shi et al. 2000) coupled

81

with the insensitivity to in vitro created lesions (Pretty 2006) indicates the unlikely influence of

the described fluorescence mechanism to explain the LUM behaviour in the present study.

Modulated LUM has previously shown a strong sensitivity to the degree of (de)-hydration of the

teeth (Jeon et al. 2008) which may be imbedded within the monotonicity of the LUM trends with

demineralization and remineralization and difficult to uncouple from actual changes in

mineralization. Baseline shifts in LUM amplitude were observed merely as a result of extended

storage conditions in the humid chamber in between treatments as shown in Appendix 5 (Fig.

A.5.1) and has been shown previously in laser fluorescence signal generation in different storage

media over time (Francescut et al. 2006). Similarly, QLF fluorescence intensity varied depending

on the degree of hydration, where light scattering was strongly influenced by the presence of

water or air within the pores. Since scattering is dictated by the enamel crystallites in relation to

their immediate environment, i.e. air or water, the refractive index contrast increases, and hence

scattering increases, as a function of drying time since a greater contrast exists between enamel

and air vs. enamel and water (Amaechi and Higham 2002; Al-Khateeb et al. 2002). It is also

important to point out the trends in LUM amplitude and phase that paralleled those of PTR,

where the largest increase in PTR amplitude yielded the largest decrease in LUM amplitude.

This effect can be explained based on the abovementioned light scattering properties and also on

the photophysical vs. photothermal processes in the trade-off between radiative and non-radiative

energy conversion efficiency, respectively. In terms of the thermal signal, enhanced light

scattering coefficients would confine the thermal centroid closer to the enamel surface yielding a

higher amplitude and smaller phase lag. In contrast, in terms of LUM, the higher optical

scattering coefficients will result in less fluorescence generation. Crystalline destruction during

demineralization will enhance the non-radiative component as excited chromophores lose their

radiative energy conversion pathways and channel the absorbed energy into non-radiative

thermal emissions. Thus, the outcome of a reduced radiative component and increased non-

radiative is a smaller LUM signal and larger PTR signal, respectively. This illustrates the

complementary nature of the generated PTR and LUM signals.

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5.3 PTR-LUM signals during short and long-term remineralization

All three remineralization treatment groups exhibited reductions in lesion depth compared to the

demineralization control group (ANOVA, p < 0.05), illustrating significant remineralization

induced by all 3 mineral solutions (Table 10). Surprisingly, no significant differences in mineral

loss were observed between the 4 treatment groups (p > 0.05). The large variance in mineral loss

of the demineralized control group may have precluded the identification of reduction in mineral

loss following remineralization. Large variation in the extent of demineralization and

remineralization was noted elsewhere (Gao et al. 1993) and attributed to small differences in

structure and mineral content between and within sections. With respect to remineralization, the

possible influence of inhibitors of crystal growth was proposed which would effectively reduce

and/or limit crystal growth on pre-existing demineralized crystallites. In the present study, the

latter effect may be enhanced by the presence of carboxymethylcellulose (CMC) in the

remineralizing solution, a common artificial saliva substitute to increase viscosity and moisten

the oral mucosa (Vissink et al. 1985). The effects of CMC on remineralization have been

associated with its ability to adsorb onto OHAp (Arèas and Galembeck 1991) and form

complexes with calcium and/or phosphate ions, the latter of which reduces the available free

mineral ions and remineralization capacity (Vissink et al. 1985). Across all 3 treatment groups

differences in PTR amplitude and phase were noted between earlier and later treatment times.

Specifically, after the 10 day exposure period in all treatment groups, amplitudes significantly

increased and phase lag decreased monotonically until the end of the treatment period. This

behaviour may be related to the known process of remineralization, the rate of which depends on

the availability of growth sites within a lesion and porosity of the intact surface layer (ten Cate

1990; Larsen and Fejerskov 1989). Furthermore, remineralization has been known to proceed via

3 main routes: the restoration of partially demineralized crystallites, growth of residual crystals

and de novo crystal formation (Yanagisawa and Miake 2003). Early on following exposure of the

demineralized lesion to supersaturated mineralizing solutions enamel porosity is high and the

surface area available for crystal growth is also large resulting in precipitation on residual enamel

crystallites (Koulourides et al. 1974; Ingram and Edgar 1994). However, once the pores in the

surface layer become occluded with precipitated mineral, diffusion fluxes across the surface

layer are retarded and remineralization of the inner lesion body is inhibited or reduced

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(Silverstone et al. 1981). Rapid initial remineralization followed by slower rates at prolonged

treatment times has been documented in the literature for decades. Johanssen (1965) found rapid

remineralization over the first 24 hours, a reduced rate over 48 hours and no further change

thereafter for 3 weeks. Gao et al. (1993) found mineral gains occurred over an 8 week period and

after 14 weeks remineralization essentially stopped. When fluoride was added to an artificial

remineralizing solution at levels between 1 – 10 ppm, maximum changes were found to occur

over a 10 day period (Silverstone 1972; Silverstone 1977). Lastly, Al-Khateeb et al. (2000)

found that remineralization varied within the first week between the different treatment groups,

with fluoride enhancing the process; however a plateau was reached thereafter. In a recent study

implementing a similar artificial remineralizing solution, preferential initial mineralization

occurred in deeper layers after 1-day of exposure, whereas after 1 week, enhanced mineralization

was noted in the outermost mineralized layers (Tanaka et al. 2009). The different rates of

remineralization in the aforementioned studies are most likely related to the use of different

remineralizing agents, enamel substrates, biological variability, and the variance in artificial

lesion production.

Although there were no significant differences between the 3 remineralization treatment groups

in terms of mineral loss and lesion depth, thicknesses derived from the theoretical fittings

pointed toward preferential remineralization of subsurface layers in the presence of fluoride. It

follows that in the absence of fluoride, surface mineral deposition was dominant, which can be

seen in the increase in surface layer thickness in layer 1 relative to layer 2 in the fluoride-free

sample (Fig. 26). The presence of a surface mineralized layer in the microdensitometric tracing

may act as a diffusion barrier preventing mineral deposition in the lesion body (Fig. 22). In the

presence of both low and high fluoride, the theory-derived thicknesses indicated that subsurface

remineralization was the dominant process and may confirm the fluoride-enhancing effect on the

remineralization process described in earlier literature (ten Cate and Arends 1977; Silverstone et

al. 1981) (compare Fig. 26 to Figs. 31 and 36). An interesting trend in remineralized samples was

the presence of phase peaks at high modulation frequencies which was manifest predominately

in the fluoride-free treatment group (Fig. 23). The large decrease in phase lag at high frequencies

occurred with a concomitant increase in amplitude across the same frequency range. In all

samples exhibiting the aforementioned peaks, mineral content depth profiles showed a high

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mineral volume in the most superficial part of the lesion (Fig. 22). Not only did the presence of

the surface mineralized layer correlate with the appearance of a smaller phase lag at high

frequencies but also correlated with the theoretical calculation of a higher scattering coefficient

in the surface layer (See Figs. 22, 23 and 24B). This is consistent with a recent PS-OCT study on

the remineralization of enamel where a highly scattering apatitic layer above the existing lesion

surface was observed after 20 days of remineralization (Can et al. 2008). Therefore, changes in

the PTR frequency response could be related to changes in the histological appearance of the

lesion and further may be useful in determining lesion activity. The LUM channel did not exhibit

a similar sensitivity at the 10 day remineralization period (Fig. 23). The high frequency of

occurrence of the surface mineralized layer in the fluoride-free group (70%) compared to the low

fluoride (40%) and high fluoride (20%) group supports the fluoride-enhanced deposition of

mineral initially in deeper layers without preferential mineralization of the outer surface,

however, further theoretical analysis of additional remineralized samples is required to validate

this conclusion.

In the present study, theoretical fitting of the final remineralized PTR amplitude and phase

curves based on thicknesses determined from densitometric tracings (Fig. 13) was used to

extrapolate and predict the demineralized lesion characteristics prior to remineralization as well

as follow the changes in opto-thermophysical properties as a function of time of exposure to the

mineralizing solutions. A summary of the main trends in opto-thermophysical parameters during

remineralization in all 3 treatment solutions is outlined in Table 11. In the presence of low-

fluoride levels (Fig. 28), a rapid decrease in amplitude across the entire modulation frequency

range and increase in phase lag at low frequency was observed for the first 10 days. A set of

derived optical and thermal parameters for the surface layer and lesion body presented different

trends as a function of treatment time (Figs. 29 – 31). The initial rapid decrease in amplitude and

increase in phase lag (Fig. 28) may be attributed to the large decrease in scattering coefficient of

the lesion body (Fig. 29B). The decrease in optical scattering coefficient may be related to the

restoration of enamel crystallinity within the lesion body, thereby reducing the acid-induced

porosity. At the crystalline level, this is consistent with the previously described mechanisms of

enamel remineralization, where the restoration of pre-existing, residual enamel crystals partially

dissolved during the demineralization process and the growth of surviving crystals are the

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favoured processes (Tohda et al. 1990; Yanagisawa and Miake 2003; Silverstone and Wefel

1981). Mineral deposition was found to account for changes in the optical properties using

polarized light microscopy by the deposition of suitably oriented OHAp crystallites (Silverstone

and Poole 1969). Crystal growth is further enhanced by the presence of low levels of fluoride in

solution (1 ppm) due to the elevated driving force for mineral deposition, in the form of FAP or

F-OHAp, in the surface and subsurface regions (Silverstone et al. 1981; ten Cate et al. 1981).

Furthermore, fluoride has been shown to have a strong affinity for apatite crystals and is

incorporated in much greater amounts in porous demineralized layers compared to sound enamel

(Koulourides et al. 1974). Low incident-photon scattering (Fig. 29B) combined with the

improvement of the thermal properties of the lesion body (Fig. 30) up to 10 days following

remineralization treatment, may support the enhanced crystallinity of the lesion body, driving the

thermal centroid deeper into the enamel. This trend is supported by the abovementioned trends in

PTR frequency response as a decrease in PTR amplitude across the entire modulation frequency

range and increase in phase lag at lower modulation frequencies (Fig. 28). The validity of the

proposed mechanism may be enhanced by the observation that LUM amplitude and phase for the

sample exposed to the low fluoride solution were strongly correlated with the derived scattering

coefficient. The rapid decrease in scattering coefficients of the lesion (Fig. 29B), a result of

enhanced crystallinity would induce longer optical path lengths and greater fluorescence

generation as is seen in the larger LUM amplitude (Fig. 28). The observed increase in the

absorption coefficient would tend to have the opposite effect, decreasing optical path lengths,

however, given the magnitude of change in the scattering coefficient compared to absorption

coefficient it is clear that the scattering depression is dominant. The larger fluorescence signal

from remineralized enamel, however, was found to be rather complex and not proportional to

total mineral uptake, a result likened to the fact that remineralization is never fully complete (Al-

Khateeb et al. 2000). LUM signals from the fluoride-free sample also exhibited trends that

correlated with the scattering coefficients. However, this was not the case in the high fluoride

group. It is important to note that remineralization of demineralized lesions may not result in

fluorescence gain equal to that lost from the enamel during lesion formation (de Josselin de Jong

et al. 2009). This is most likely attributed to the heterogeneity in the demineralized enamel which

will induce scattering properties unique to individual samples. Furthermore, this is supported by

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the fact that in some cases mineral is not deposited in a crystalline prismatic form as in sound

enamel, but rather in amorphous deposits which can influence scattering properties. An

additional influence to overall fluorescence generation is the hydration level of the sample as

described earlier for demineralized lesions. The dehydration rate of highly remineralized enamel

was found to occur at a much lower rate than sound and demineralized enamel (van der Veen

and de Josselin de Jong 2000). As drying times for all samples remained constant irrespective of

treatment, it may be possible that residual water left within the enamel pores influence the

overall fluorescence generation. Replacing water-laden interprismatic pores with air increases

the refractive index difference between the enamel prisms and the surrounding environment

which in turn increases the scattering coefficient. Therefore, the hydration state of enamel is an

important confounding factor that significantly affects LUM signal generation, manifested as

baseline shifts. The hydration state may have a similar effect on PTR signal generation. The high

infrared absorption coefficient of water (Fig. 7) compared to air would significantly attenuate the

emitted photothermal signal.

During prolonged treatment times in all 3 mineralizing solutions (i.e. after 10 days), PTR

amplitude and phase trends reversed direction resulting in a monotonic increase in amplitude

with a smaller phase lag (Figs. 23, 28 and 33). This may be attributed to the random orientation

of deposited crystals as well as de novo mineral precipitation within the surface layer and lesion

body, particularly within the interprismatic regions, a function of the lower specific surface area

of the crystalline mineral phase (Yonese et al. 1981; Amjad et al. 1981; Palamara et al. 1986).

An amorphous mineral phase would generate additional scattering centers through the larger

number of crystal grain boundaries effectively increasing the scattering coefficient and creating

poorer thermal properties as the density increases, both trends which were observed in the

theoretical fittings (Figs. 24b, 25, 29b and 30). Furthermore, in Figs. 25, 30 and 35, a decrease in

thermal properties at the final demineralization point or during the first 2 days of

remineralization, was followed by a transient increase, and a further decrease at prolonged

treatment times, an effect likened to competing thermal processes during the remineralization

period. Higher absorption coefficients calculated after the 10 day remineralization period in the

fluoride-free (Fig. 24A) and low fluoride group (Fig. 29A) may substantiate the proposed

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amorphous mineral precipitation, and has been documented in an earlier study (Krutchkoff and

Rowe 1971). Longer exposure periods in a CMC-containing remineralizing solution were found

to significantly impede remineralization compared to non-CMC control solutions, an effect

related to the complexation of solution calcium and phosphate ions (Tschoppe et al. 2008). A

similar finding was observed by Amaechi and Higham (2001) where a remineralizing solution

without CMC, and identical in all other components, showed a greater remineralizing capacity.

Therefore, the documented effects of CMC, as described earlier, may roughly mimic intraoral

remineralization processes, as many salivary proteins have a high affinity for OHAp and

significantly regulate the available calcium and phosphate levels (Hicks et al. 2003). At later

remineralization times in the fluoride-free and low fluoride group, a greater thermal mismatch

was evident between the surface layer and subsurface layer (Figs. 25 and 30). The same trend

was also evident in the 40-day demineralized sample (Fig. 20d). As the surface layer becomes a

better conductor and diffuser, thermal energy will propagate rapidly toward the L1 - L2 interface.

However, since the properties of the subsurface layer are so poor, thermal fluxes are significantly

impeded and as a result, thermal energy will accumulate at the boundary. Effective confinement

of the thermal centroid will then occur within the surface layer thereby resulting in the observed

increase in amplitude and smaller phase lag as the reaction moves closer to the enamel surface.

This may suggest an amplification of the dominant surface reaction whereby the effects of the

underlying enamel at later remineralization times are concealed. Furthermore, this may imply

that once the surface layer reaches a critical thickness its properties dominate the thermal

response at the expense of the underlying enamel, which may require lower frequencies (longer

thermal wavelengths) to probe deeper regions. The observed surface deposited mineral which

was most prevalent in the fluoride-free group (Fig. 22) may chemically amount to a diffusion-

barrier generating an impedance of inorganic mineral ion diffusion into deeper layers, while at

the same time driving the thermal-wave centroid closer to the enamel surface, apparent in the

increasing amplitude and smaller phase lag. After the first 10 days of remineralization, changes

in thickness were minimal (Figs. 26, 31 and 36) but rather significant changes in the optothermal

transport properties were dominant. These changes may indicate the shifting thermal centroid

from deeper within the enamel during earlier exposure periods, when ingress and precipitation of

mineral ions to restore crystallinity and reduce thicknesses of deeper layers is enhanced, toward

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the enamel surface at prolonged treatment time. Larger absorption coefficients at later exposure

periods in the surface layer (layer 1) may further support surface dominated reactions as the

major contributor to the PTR signal (Figs. 24A and 29A).

PTR-LUM frequency responses and theoretical fittings of the high fluoride sample displayed

trends that deviated from the low and fluoride-free samples. In the latter samples, rapid changes

in thermal properties occurred over the first 10 days which was followed by an inversion and a

large thermal mismatch at later remineralization times (>20 days) (Table 11). A decrease in

amplitude following the first 10 days of remineralization, predominately at low modulation

frequencies, was accompanied by a near-monotonic decrease in phase lag across the same

frequency range (Fig. 33). This may suggest significant mineral deposition within the lesion

body such that the regression in the thickness of the subsurface layer progresses from the

advancing front of the lesion toward the surface layer. If the lesion following demineralization

had a certain thermal centroid at a given frequency and during subsequent remineralization the

thickness of the subsurface layer decreased with minimal changes in the thickness of the surface

layer, as was shown in the thicknesses derived from the theoretical model (Fig. 36), then as the

subsurface layer becomes thinner the thermal centroid will be maintained within the layer as it

shifts closer to the surface. Klinger and Wiedemann (1985) found that after a 93 hour immersion

of demineralized lesions in a calcium phosphate solution, the bottom of the lesion moved toward

the enamel surface. In contrast, the low fluoride sample showed mineral gains in both surface

and subsurface layers over the first 10 days (Fig. 32). The higher fluoride concentrations would

be expected to diffuse rapidly into deeper areas within the porous demineralized enamel thereby

increasing total fluoride within the lesion to enhance mineral accumulation. After 10 days of

exposure to the high fluoride solution a marked reduction in the thermal properties of both layers

was evident (Fig. 35). This was accompanied by an increase in the absorption coefficient (Fig.

34A) and an increasing scattering coefficient (Fig. 34B) which was expected since an opaque

and chalky macroscopic appearance of enamel was observed after the 4-week immersion in the

high fluoride solution (Fig. 21c). The surface hypomineralization observed in the mineral content

depth profile of the high fluoride group may be a result of surface mineral loss during the

demineralization process, the fluoride-enhanced driving force for subsurface remineralization

and/or the deposition of a surface material of a different phase. The latter 2 processes may be

89

likely due to the high fluoride concentrations implemented (1000 ppm), where a calcium

fluoride-like phase may precipitate (Larsen and Fejerskov 1978). The formation of calcium

fluoride-like material on enamel surfaces, a reaction mechanism between fluoride and enamel

known to break up the crystal lattice, may occur; however this process is enhanced under acidic

pH conditions (Kidd and Joyston-Bechal 1980). CaF2 is a relatively less stable phase compared

to FAP and F-OHAP under normal oral conditions (Mellberg and Mallon 1984). In the presence

of phosphate ions the CaF2-like deposits may be hydrolyzed to F-OHAp (Larsen and Richards

2001; Ogaard 2001). Additionally, a HF-induced etch of the enamel surfaces may occur,

however, given the neutral pH of the remineralizing solution, the concentration of HF would be

rather small. The chemical behaviour in the presence of high fluoride, manifested as a surface

hypomineralization, is supported by the minimal change in PTR-derived thickness of the surface

layer thickness over the remineralization period. Furthermore, the poorer thermal properties

generated at prolonged remineralization times may reflect a surface precipitate. If a precipitate

was formed at the enamel surface following fluoride exposure, the level of integration of this

layer with the underlying enamel could not be determined from microradiographic analysis.

5.4 Errors and Limitations in the extraction of opto-

thermophysical properties

Historical methods for extracting optical and thermal properties from enamel require the use of

thin sections of known thickness. In terms of thermal diffusivity measurements, it has been

shown that the different preparation methods of samples resulted in significantly different results

(Panas et al. 2003). Furthermore, sectioning enamel can disrupt its crystalline ultra-structure and

induce micro-cracks which can significantly affect the optical properties determined from

transmission and reflection measurements. Thus, sample manipulation on its own can induce

significant changes in optical and thermal properties of the tissue, adding a source of variability

on top of the inherent intra and inter-sample local differences in structure (Panas et al. 2007).

Spitzer and ten Bosch (1977) determined the absorption and scattering coefficients of enamel

slabs as a function of demineralization time, however, large errors in the absorption coefficient

(> 40%) were observed. Furthermore, they estimated that error from the determination of the

optical properties from one sample is about 60%. Scattering and absorption coefficients

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determined by comparing the scattering data with Monte Carlo light scattering simulations of

enamel sections in a study by Fried et al. (1995) found an error of 30% for all scattering

coefficients. Ko et al. (2000) used reflection and transmission measurements from enamel

sections calculated according to Kubelka-Munk equations to derive optical scattering

coefficients. The authors found a 28% variation in the scattering coefficients. In terms of the

latter 2 studies, variations in the optical coefficients were attributed to lesion heterogeneity,

including the influence and composite nature of the intact surface layer, and intra- and inter-

sample variability. An estimation of the error in the theoretical program due to experimental

error of PTR signal measurement is presented in Appendix 4. The percentage difference in the

scattering coefficient is on the order of those described in the aforementioned literature (Table

A.4.1). Additional sources of error in the theoretical extraction of opto-thermophysical

parameters may be influenced by the variable rates of sample de/hydration, small microstructural

differences within and between samples and also by the crude 3-layer representation of the

complex caries lesion. In an earlier study implementing standardized drying times, lesions

varying in severity also exhibited different de-hydration rates (Lagerweij et al. 1999). Thus,

larger lesions and/or lesions with remineralized surface layers, which may dry at slower rates

compared to smaller lesions, may result in more residual water occupying enamel porosities

thereby influencing PTR frequency response and optical and thermal property extraction (van der

Veen and de Josselin de Jong 2000). The delineated layers of the caries lesion are not perfectly

reflecting and transmitting interfaces, but rather based on the accumulation or depletion of

thermal energy. In reality, 3 effective layers may not approximate the multi-layered caries lesion,

however, the introduction of additional layers is computationally intensive and the lengthy

calculation time currently imposed for the 3-layer system would be further increased. Earlier

studies attempting to indirectly model physical phenomena during demineralization processes are

generally restricted to a 2-layer approximation (Mujat et al. 2003; Zijp 2001). The surface layer

was neglected as its thickness was typically small compared to the thickness of the demineralized

lesion. As discussed early on, attempts to fit the present demineralized and remineralized PTR

data to a 2-layer approximation yielded a very poor fit of the experimental and theoretical curves.

Thus, the contribution from the intact surface layer was significant enough so that optical and

thermal properties of the layer were considerably different from the lesion body and contributed

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to the overall PTR amplitude and phase frequency response. The present study illustrates the first

account where demineralized and remineralized enamel could be resolved into 3 effective layers,

where the non-destructive extraction of opto-thermophysical parameters of each layer allowed

for depth-profile reconstruction as a function of treatment time.

5.5 Comparison of irradiation wavelengths and future directions

A comparison of the PTR frequency response under both irradiation wavelengths (660-nm and

830-nm) revealed similar trends across the entire modulation frequency range. The fact that

similar trends were evident under 830-nm laser radiation (Appendix 1) may implicate the longer

wavelength laser light as an effective light source for evaluating sound, de- and remineralized

enamel. Thus, the 830-nm laser may be used as a viable alternative to the 660-nm laser and/or

used as a dual wavelength PTR probe, which would further enhance the depth profilometric

character of PTR by yielding additional amplitude and phase signal channels. The advantage of

the longer wavelength laser light is the deeper penetration of the optical field as absorption and

scattering coefficients are lower than smaller wavelengths (see Table 1). As a result, deeper

subsurface features may be resolved with the longer wavelength light. However, a disadvantage

of the longer wavelength light is the lower SNR, as can be seen in the PTR frequency responses

(Appendix 1).

Qualitative evaluation of PTR frequency response may provide a rough estimate of lesion size.

The PTR phase peak at low modulation frequencies, of the 10-day (Fig. 16) and 40-day

demineralized samples (Fig. 17), indicate thermal wave interference patterns occurring within

the demineralized lesion. Calculating the thermal diffusion length at the frequency of the phase

maxima may therefore be a rough estimate of lesion depth. For example, in the 10-day

demineralized sample phase maxima appear at ≈8 Hz, and in the 40-day demineralized sample at

≈5 Hz. Given the thermal diffusivity of the lesion body for the 10-day and 40-day samples, 3.3 x

10-7

and 2.3 x 10-7

m2/s, respectively, thermal diffusion lengths are ≈114 µm for the 10-day

sample and 121 µm for the 40 day sample. These estimates are close to the values of the 10-day

lesion (88.6 μm) and 40-day lesion (114.8 μm) determined by TMR. However, following a

single frequency scan, the thermal diffusivity is an unknown parameter and as a result thermal

diffusion length cannot be predicted as easily. In the present study, layer thicknesses were

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validated using TMR where microdensitometric tracings were used as guidelines to define the

thicknesses limits in the theoretical program. Clinically, final thicknesses are clearly unavailable

and therefore the robustness of our theoretical/computational program would beneficially yield

good estimates of lesion parameters, irrespective of the initial set of parameter value ranges.

Given the reliability of the calculated thicknesses outlined in the previous paragraph, in the

future refinement of the theoretical program and fitting procedure, different programs may be

designed based on the overall size of the lesion. Thus, the PTR phase, which has emerged as the

most sensitive channel to the depth-dependent changes, may be used in vitro or in vivo as an

initial screening channel in order to roughly estimate lesion depth, after which the specific

theoretical program can be implemented based on the aforementioned phase behaviour to extract

the relevant opto-thermophysical parameters.

5.6 Summary

In summary of the trends described above, PTR and LUM in backscatter mode were sensitive to

the formation of mineralized layers during de- and remineralization. At the initial state, PTR

signals and the combined theoretical model indicated that sound enamel is a complex multi-

layered substrate where an aprismatic layer at the surface of the enamel with different optical and

thermal properties must be considered. At the onset of demineralization, an increase in PTR

amplitude and decrease in phase lag in was observed with a monotonic depression in LUM

signals. Multi-parameter fits of PTR experimental data revealed a marked increase in optical

scattering coefficients and the generation of poorer thermophysical properties during

demineralization consistent with crystalline disintegration and formation of subsurface

microporosities. Changes in LUM signals could be explained based on the enhanced light

scattering properties of demineralized enamel and the channelling of radiative to non-radiative

energy sources caused by the loss of inorganic structure. Trends in opto-thermophysical

parameters during demineralization indicated that artificial caries lesions involve a dynamic

surface dissolution– reprecipitation mechanism during subsurface lesion formation. Trends in

PTR signals and opto-thermophysical parameters during the remineralization phase indicated a

multi-factorial and complex repair process. This was considered as interplay between shifting

thermal centroids as mineral gains in surface and subsurface regions alter the opto-

thermophysical properties of the effective layers as a function of remineralization time. The

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theoretical model pointed to a fluoride-enhanced remineralization of the lesion body, however,

no statistically significant differences in TMR defined mineral loss and lesion depth were noted

between the remineralization treatment groups. Lastly, the high fidelity and uniqueness of the

fitted parameters illustrates the effectiveness of the computational algorithm and its potential

applicability toward the non-destructive quantification of lesion thicknesses and the

reconstruction of opto-thermophysical depth profiles.

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CHAPTER 2: Transmission mode PTR – LUM

6 Rationale

In the first chapter of this project PTR and LUM were investigated in back-propagation mode

where sample treatment was interrupted periodically during the test period in order to be

analyzed. Sample interruption, coupled with the washing and drying periods and the storage in

the humid box may add additional sources of variability to the experimental protocol,

predominately as changes in water content can significantly influence PTR and LUM signal

generation. The influence of external water-based solutions on infrared emissions was initially

observed during preliminary measurements where the ability of backscatter-mode PTR was

assessed to monitor changes in enamel in real-time during continuous exposure to the treatment

solutions. The results of this satellite experiment revealed the inability of mid-IR photons to

penetrate the water-based demineralizing and remineralizing solutions; a result attributed to

strong water absorption bands in the mid-IR spectral range (Fig. 7). This prompted realignment

of the experimental setup to consider PTR-LUM transmission experiments. The advantage of the

transmission PTR-LUM system is that indirect measurements of mineral loss can be monitored

during the treatment process without sample interruption.

An extensive review of in vitro de- and remineralization literature revealed only a limited

number of reports, by a single research group, concerned with directly monitoring enamel and/or

dentin demineralization and/or remineralization continuously in real-time (Gao et al. 1991; 1993;

1993a; Anderson and Elliott 1992; Anderson et al. 1998, 2004). An ingenious set of experiments

conducted by the aforementioned research group, modified the conventional microradiographic

system to include a photon-counting system, which allowed for the increased frequency of

mineral-content measurements on relatively thick (≈350 µm) sections for direct real-time mineral

quantification during demineralization and remineralization treatments (Anderson et al. 1998).

Typically, the protocol employed in vitro to study demineralization-remineralization phenomena

often involves the use of multiple thin enamel sections each delineated with nail varnish to

maintain a region of sound tissue, and interrupted repeatedly for analysis. Thus, direct or indirect

measures of mineralization are evaluated when the sections are in a static state. As both

demineralization and remineralization are kinetic, time-dependent processes, significant sample

95

interruption can affect both the rate and extent of lesion formation. Furthermore, the use of

multiple sections introduces additional biological variability where each sample may exhibit

independent rates; a function of the composite nature of enamel and the diverse history in the

complex oral environment. Consequently, the ability to monitor changes in a tooth as a function

of time with minimal disturbance would be ideal, as both reliability and controllability of the in

vitro treatment method would be improved. However, due to technical difficulties in the

experimental setup and validation techniques, real-time studies have been challenging and not

often explored.

The combined PTR - LUM system has demonstrated sensitivity to characterize the disease state

of dental tissue in the backscatter-mode. The objective of the present study is to assess the ability

of the PTR-LUM system to monitor changes in real-time during de- and re-mineralization

processes.

7 PTR-LUM Transmission-Mode: Materials and Methods

7.1 Sample Preparation

Five intact and sterilized samples (gamma irradiated, 4 kGy) that were visually identified as

sound without the presence of defects, caries lesions or stains were sectioned in half

mesiodistally. The experimental protocol was approved by the University of Toronto Ethics

Review Board (Protocol #25075). The anatomical surface of the sectioned enamel was left intact

while the cut side of the section was ground sequentially using successively finer grits of

waterproof SiC paper under constant water exposure (320-b to 1200-b waterproof SiC paper).

Sections were ground to an average thickness of about 1.25 mm.

An opening was created on one wall of a container (25 cm3) matching both the size and shape of

the cut section. The enamel section was inserted into the cut wall and fixed in position with

utility wax, such that the enamel surface is in constant contact with de- and re-mineralizing

solutions. The intact enamel surface was positioned facing laser irradiation and the polished

surface oriented facing the off-axis mirrors (Fig. 2.1). Containers were fixed on LEGO bricks

and placed on the micrometer stage such that the intact enamel surface was at the focal plane of

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the incident laser light. The size of the delimited window exposed to the treatment solutions was

approximately 2 mm x 2 mm.

Figure 2.1. Experimental apparatus for transmission experiments. Laser beam is incident on the

enamel surface.

7.2 PTR-LUM frequency scans

Frequency scans similar to those in experiment 1, described in detail above, were run initially on

intact enamel samples under 670-nm laser radiation. The modulation frequency range was from 1

Hz to 1000 Hz. The number of data and cut off points for PTR were increased to 25 and 12,

respectively. Corresponding data and cut-off points for LUM measurements were 40 and 15,

respectively. LUM data acquisition was alternated between the transmission and backscatter

mode. PTR Measurements commenced at the first exposure to the demineralizing gel. Two

samples were treated simultaneously; alternating frequency scans every 3 hrs, allowing 20 min of

thermal stabilization time prior to scanning. Immediately following the initial immersion of

demineralizing gel and remineralizing solution, measurements were performed every 30 min for

7 hours. As the MCT detector sensing element requires liquid nitrogen cooling, samples were

neither scanned overnight, nor over weekends. Sections remained under constant solution

exposure during these periods and the total time was factored into overall treatment time.

Individual samples were left undisturbed and containers were sealed during the treatment and

measurement processes.

97

7.3 Demineralization and Remineralization Treatments

Demineralization and remineralization treatment groups are shown in Table 2.1. Enamel sections

were demineralized in 25 mL of the same acidified gel solution as described in Experiment 1

(Section 1.4.1). Total demineralization time was 15 days. After the final PTR-LUM

measurement during demineralization, the gel was carefully suctioned out of the container using

a syringe, while the sample container remained on the sample stage. Containers were washed

through with 20 rinses of distilled water to remove gel particulates adsorbed on the enamel

surface and container walls. After a drying period of 1 hour, 25 mL of a remineralizing solution,

containing 1 ppm fluoride, was decanted and measurements resumed for an additional 20 days.

The remineralizing solution constituents are the same as presented in Table 4.

Table 2.1. Treatment groups for transmission-mode PTR-LUM study (n = 10).

7.4 PTR-LUM Experimental Setup

A diagrammatic representation of the experimental setup for transmission measurements of

enamel sections is illustrated in Fig. 2.2. This setup is modified from backscatter PTR-LUM

setup by the addition of a higher power laser diode (500 mW; 800 mA; Sony SLD 1332V) fixed

in a laser diode mount (Thorlabs TCLDM9) and positioned behind the 3-axis translational

sample stage. The laser beam was focused to a spot size of 590 μm. An opening created where

the polished surface contacts the container walls allowed transmitted infrared emissions to be

collected by the off-axis paraboloidal mirrors and focused on a MCT detector. Transmitted

modulated luminescence signals were collected using the same photodetector setup as the

backscatter PTR-LUM experimental mode. An additional photodetector was positioned on the

same side of laser irradiation in order to collect back-scattered LUM emissions through the

treatment solution.

Treatment Group Demineralization treatment (Days)

Remineralization treatment (Days)

Sample size

Demineralization 15 ----- 5

Mineral solution (1 ppm fluoride)

15 25 5

98

Figure 2.2. Experimental setup for transmission-mode PTR-LUM.

7.5 Transverse microradiography (TMR) and image analysis

At the completion of all transmission PTR-LUM measurements all samples were

microradiographed, in the same manner as detailed earlier, to determine the mineral loss and

depth of the artificially demineralized and remineralized lesions.

8 Results

8.1 Time-series demineralization experiments

An exemplary artificial caries lesion, characterized by a thin, intact surface layer, superficial to a

deep subsurface lesion body was created following demineralization of enamel sections and is

shown in Fig. 2.3. Mineral loss and lesion depth of the presented lesion was 3750 vol%.μm and

98.5 µm, respectively. PTR and LUM amplitude and phase signals at 1 Hz, plotted as a function

of time, for the demineralized lesion in Fig. 2.3 revealed monotonicity with treatment time (Fig.

2.4). A decrease in PTR amplitude with a concomitant increase in PTR phase lag occurred from

the initial acid gel exposure period over the course of 15 days. Following an initial transient time

lag lasting approximately 15 - 20 hrs PTR amplitude decreased and phase lag increased linearly

up to about 75 hrs. A reduced rate and a slope change followed 75 hrs of demineralization until

the treatment conclusion. Time-series changes in transmission-mode LUM amplitude and phase

signals at 89 Hz, the frequency of LUM phase minima, are displayed in Fig. 2.4. LUM signals

mirrored those of PTR throughout the duration of the treatment period.

Photodiodes and optical filters

SampleLaser Diode Module

Off- axis Mirrors

IR Detector

Off-axis mirrors

Pre-Amplifier

HgCdTe Detector

Lock-in Amplifier

Optical filter & Photodetector

Laser Driver Waveform

Sync. Signal

Sample Apparatus

Computer

Internal

Generator Function

Amplifier Lock-in

Optical filter & Photodetector

Laser Diode and Module (670 nm)

99

Figure 2.3. Exemplary microradiograph (a), densitometric tracing (b), and visible light

transmission image (c) of a demineralized enamel section. Mineral loss and lesion depth were

determined as 3750 vol%.μm and 98.5 µm, respectively.

Figure 2.4. Time-series transmission-mode PTR-LUM amplitude and phase signals at 1Hz

(PTR) and 89Hz (LUM) for a sample demineralized for 15 days.

100µm

(A) (B) (C)

0 50 100 150 200 250 300 3500.006

0.008

0.010

0.012

0.014

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0.020

0.022 PTR Amplitude

Am

plit

ud

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a.u

.)

Time (hrs)

0 50 100 150 200 250 300 350

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-100

-95 PTR Phase

Ph

ase

(D

eg

)

Time (hrs)

0 50 100 150 200 250 300 350

0.20

0.22

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0.30LUM Amplitude

Am

plit

ud

e (

a.u

.)

Time (hrs)

0 50 100 150 200 250 300 350

-16.4

-16.0

-15.6

-15.2

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-14.4 LUM Phase

Ph

ase

(D

eg

)

Time (hrs)

100

8.2 Time-series remineralization experiments

At the onset of the remineralization treatment period, a step-decrease in phase lag at 1 Hz was

accompanied by a concomitant increase in amplitude (Fig. 2.5). This behaviour occurred for a

period of ≈200 hrs since the start of the mineral solution exposure, after which amplitude and

phase signals reversed direction and reached stable values after ≈650 hrs until the end of the

exposure period. LUM amplitude and phase at 89 Hz, the frequency where LUM phase minima

appear, reveal similar trends as PTR however, exhibited less marked changes at the onset of

mineral solution exposure. Visible light transmission images reveal the non-uniform appearance

of remineralized enamel, with regions of mineral restoration intertwined with more opaque

regions of demineralization. Microradiographs and mineral content depth profiles of an

additional demineralized and remineralized sample is presented in Fig. 2.6; corresponding PTR-

LUM signals are shown in Fig. 2.7. The lesion displayed a relatively thick remineralized intact

surface layer of ≈15 µm superficial to a deep subsurface lesion ≈124 µm with an exceedingly

large amount of mineral loss (5370 vol%μm) (Fig. 2.6). Following the exposure to the

mineralizing solution, PTR amplitude at 1 Hz (Fig. 2.7A) exhibited a step-increase for ≈300 hrs

which occurred with a concomitant decrease in phase lag. After ≈300 hrs of remineralization

amplitude signals decreased below those of the final demineralization and remained near-

constant for the rest of the treatment period excluding a slight increase in the final ≈100 hrs.

Transmission LUM signals at 89 Hz revealed similar trends as the PTR at 1Hz during the

demineralization phase (Fig. 2.7B). At the onset of the remineralization phase, a slight increase

in amplitude occurred for the first ≈100 hrs with no discernible changes in phase. At later

remineralization times a gradual decrease in amplitude and phase were noted until the end of the

treatment period. Time-series LUM in backscatter mode at 89Hz monitored the effects at the

enamel surface through the demineralizing and remineralizing solutions. During the

demineralization phase, LUM amplitude and phase decreased for the first ≈175 hrs and increased

thereafter (Fig. 2.7C) consistent with the slope changes in both transmission PTR and LUM

signals (Fig. 2.7A, B). At the onset of remineralization, an increase in amplitude and phase

paralleled the increase in PTR amplitude and decrease in phase lag (Fig. 2.7C). This was

followed by a marked decrease in both LUM amplitude and phase after ≈600 hrs. A slight

101

increase was observed again for the last ≈100 hrs as noted for PTR amplitude and phase and

opposite the trends in transmission LUM.

Figure 2.5. Time-series transmission PTR-LUM amplitude and phase signals at 1Hz (PTR) and

89Hz (LUM). Vertical dashed lines divide de-and remineralization treatments. The visible light

transmission image (top right) and microradiographic image (bottom right) are presented in the

adjacent figures. Mineral loss = 1010 vol%.μm; Lesion depth = 61 μm.

Figure 2.6. Microradiograph and mineral content profile of a de- and remineralized sample. The

corresponding PTR-LUM signals are presented in Fig. 2.7. Mineral loss = 5730 vol%.μm;

Lesion depth = 139.4 μm.

100 µm

102

Figure 2.7. Time-series transmission PTR signals at 1 Hz (A) and transmission LUM at 89Hz

(B). (C) Time-series LUM signals at 89 Hz viewed in backscatter mode. Vertical dashed lines

divide de-and remineralization treatments. The corresponding microradiograph and mineral

content depth profile is presented in Fig. 2.6.

9 Discussion

9.1 PTR-LUM signals and time-series demineralization

Exposure to the demineralizing solution generated a mineral distribution with a large mineral

loss to lesion depth ratio, as depicted in the microradiograph (Fig. 2.3). Both PTR and LUM

signal channels exhibited monotonic decreases over time (Fig. 2.4). The decrease in PTR

amplitude over time can be explained based on the generation of a near surface layer, most likely

the demineralized lesion, with poorer thermal properties and higher scattering coefficients, as

was shown in Chapter 1. In transmission-mode, thermal confinement closer to the enamel

surface means non-radiative conversion reactions are occurring farther away from the IR detector

and the result is a smaller amplitude and larger phase lag of the generated photothermal response.

Furthermore, higher scatter of the photon density field from the onset of demineralization

effectively impedes photon path lengths, confining the thermal-wave centroid to a narrower

surface region. This will have a marked effect on both PTR and LUM signal generation, as less

thermal and optical energy is available for transmission through the thin enamel section. As

0 200 400 600 800 1000

0.23

0.24

0.25

0.26

0.27

0.28

0.29

0.30

0.31

Demin Remin

LUM Amplitude

Am

plitu

de

(a

.u.)

Time (hrs)

0 200 400 600 800 1000

-16.2

-16.0

-15.8

-15.6

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-14.8

-14.6

-14.4

Demin Remin

LUM Phase

Ph

ase

(D

eg

)

Time (hrs)

0 200 400 600 800 1000

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

Demin Remin

LUM Amplitude

Am

plit

ud

e (

a.u

.)

Time (hrs)

0 200 400 600 800 1000

-6

-5

-4

-3

-2

-1

0

1

2

3

4

Demin Remin

LUM Phase

Ph

ase

(D

eg

)

Time (hrs)

0 200 400 600 800 1000

0.010

0.011

0.012

0.013

0.014

0.015

0.016

PTR Phase

PTR Amplitude

Remin

ReminDemin

Demin

Am

plit

ud

e (

a.u

.)

Time (hrs)

0 200 400 600 800 1000

-122

-120

-118

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Ph

ase

(D

eg

)

Time (hrs)

(A) (B) (C)

103

described earlier, sound enamel contains a unique structural alignment of inorganic prisms

running almost perpendicular to the enamel surface. Where the prisms run perpendicular to the

enamel surface, incident light shines directly on enamel crystallites and is transmitted deeper into

the tooth in a manner analogous to optical fibres (Odor et al. 1996). From the onset of

demineralization, ultrastructural changes in enamel, such as the widening of interprismatic

spaces, result in larger surface and subsurface layer porosity which act as scattering centers,

while at the same time the small microchannels are significant impedances to heat flow. A

combination of both effects, which manifest themselves as a marked increase in the scattering

coefficient in the lesion and poorer thermal properties, result in a shift of the thermal centroid

closer to the enamel front surface. At early demineralization times the optical and thermal

contrast between the surface layer, lesion body and sound underlying enamel would be minimal.

As a result, surface mineral loss combined with subsurface mineral loss would confine the

thermal centroid closer to the near surface, while allowing significant thermal-wave propagation

beyond the lesion body - sound enamel interface. However, once the lesion grows to the size

evident in Fig. 2.3, a marked thermal discontinuity would be expected between the lesion zones

and as a result inter-reflections within the surface and lesion body would increase the density of

photons within the lesion body, confining both optical diffuse photon field and the thermal-wave

centroid to this region, and reducing the amount of thermal-wave transmission beyond the lesion

body – sound enamel interface.

A rapid decrease in amplitude and phase of both PTR and LUM occurred for about the first ≈75

hrs following exposure to the demineralizing solution. The initial rapid rate of decline in both

signals may be attributed to surface and subsurface mineral loss under the acid challenge. The

initial dissolution may occur directly at the enamel surface causing an increase in surface

roughness, which would effectively confine photons and thermal waves to a narrower surface

region reducing the efficiency of the transmitted signals. Following the first rapid decline in

PTR-LUM amplitude and phase signals, a level of saturation appeared; however, following ≈125

hrs, a second rapid decrease in PTR and LUM signals was evident (Fig. 2.4). This trend may be

analogous to that described in earlier studies where an initial sigmoidal-shaped distribution of

mineral loss over time was evident over the first 45 - 78 hrs (Anderson et al. 1998). Furthermore,

Gao et al. (1993a) also found similar trends, however, those authors found that the initial

104

demineralization rate was much higher, which is more consistent with the initial rapid rate of

PTR-LUM signal decline over the first ≈50 - 75 hrs (Fig. 2.4). Initial rapid demineralization was

followed by a slope decrease after ≈44 hrs, which they interpreted as the initial surface layer

formation, and further followed by a lower rate of demineralization related to the progression of

the subsurface lesion without any further change in the thickness of the surface layer. As a result,

the initial mineral loss distribution over time was sigmoidal in shape. It may be likely that the

initial rapid decrease in PTR-LUM signals followed by a transient decrease in the rate of signal

progression until about ≈125 hrs represents the sigmoidal-shaped distribution of mineral loss

described above. The initial demineralization period was observed in several studies and

explained based on a combination of factors, including natural enamel surface properties, which

maintain higher fluoride levels than underlying enamel, the formation of the subsurface lesion

and/or the dynamic process of intact surface layer formation (Anderson et al. 1998; Gao et al.

1993a; Anderson et al. 2004; Yamazaki et al. 2007). Therefore, it is likely that the same initial

period, where PTR and LUM signals rapidly decreased is characterized by a combination of

processes including the dynamic mineral loss-mineral gain of the intact surface layer occurring

with concomitant mineral loss from the subsurface lesion, as was evident in the results of

Chapter 1. Interestingly, the duration of the initial demineralization period was very similar in all

demineralized sections, particularly with respect to the PTR phase signal channel. Comparing the

3 demineralized sections in Figs. 2.4, 2.5 and 2.7A, the duration of the initial demineralization

period ranged from ≈75 - 125 hrs. This range was typical among all other demineralized enamel

sections not displayed. The reproducibility of the initial demineralization period was also

observed by Anderson et al. (1998), where a similar duration of the sigmoidal-shaped period of

mineral loss was found for all samples. A discrepancy in the duration of this initial period in the

present study compared to the earlier studies is presumably due to the stronger acid challenge

and constant-composition conditions in the earlier study. This would explain why the duration of

the initial period in the present study appeared much longer. The fact that this initial

demineralizing period has only been observed in few studies may be due to the nature of the

investigative technique in the present study, where real-time indirect measures of mineral content

were employed over short (≈20-min) intervals during the demineralization process in a non-

invasive manner. Following the initial demineralization period PTR and LUM signals decreased

105

in a near-linear fashion. This is similar to the observations in the earlier studies, where following

the initial sigmoidal-shaped mineral loss over time a linear distribution of mineral loss over time

was observed (Anderson et al. 1998; Gao et al. 1993a; Anderson et al. 2004). The authors

purported the linear period to subsurface mineral loss, which continued until the end of the

treatment period. Furthermore, the observation of a linear period indicated that reactions at the

dissolving crystal surfaces of the advancing lesion front were the rate-limiting processes in lesion

formation (Anderson et al. 1998). The rapid decrease in PTR signals following the initial

demineralization period may also suggest that the dominant mechanism is the mineral loss

occurring primarily from the subsurface regions. This is supported by the fact that a marked

decrease in mineral volume can be seen in the subsurface layer of demineralized enamel

sections. However, significant deviations from linearity were observed in the PTR signal

decrease over time. These deviations may suggest that lesion formation in enamel sections

cannot strictly be attributed to a single controlling mechanism, i.e. surface or diffusion –

controlled, but rather a combination, or continuum, of rate controlling processes (Elliott et al.

2008). Furthermore, in the present study, a reduction in the rate of PTR and LUM signal

decreases occurred near the end of the demineralization period, which is in contrast to the earlier

studies where the linear period extended until the end of the acid challenge (Anderson et al.

1998; Gao et al. 1993a; Anderson et al. 2004). This is most likely a function of the increased

mineral accumulation within the demineralizing gel over time which may cause an increase in

the degree of saturation of the demineralizing gel with respect to enamel mineral and lower

driving force for subsurface mineral loss. Furthermore, PTR signal deviation from linearity at

later demineralization times may be related to the local structural differences in enamel within

one section and between sections (Gao et al. 1993a; Anderson et al. 1998). This is particularly

evident in the present study where natural enamel surfaces remained intact and significant

variation in the structural and chemical properties of the surface enamel layer compared to the

underlying enamel are expected. The overall transition from the ‗initial‘ demineralizing period to

the ‗later‘ demineralization period may be related to shifting thermal centroids during the process

of lesion formation, where initial rapid mineral loss may shift the thermal centroid closer to the

surface while at later times the centroid is maintained within the growing demineralized lesion.

106

9.2 PTR-LUM signals and time-series remineralization

At the onset of remineralization, a transient step-decrease in PTR phase lag was accompanied by

an increase in amplitude (Figs. 2.5 and 2.7A). After ≈300 hrs amplitude and phase signals

reversed direction and reached stable values after ≈650hrs until the end of the treatment period

(Fig. 2.5). The second remineralized sample shown in Fig. 2.6, showed a less marked decrease in

phase lag and increase in amplitude over a similar period (Fig. 2.7A). This behaviour may reflect

the mechanism of fluoride enhanced remineralization, promoting rapid uptake and precipitation

of mineral ions from solution within the entire lesion depth. Subsurface remineralization

processes may only occur for a transient period, i.e. the first 10 days, whereas surface mineral

deposition may be dominant at later times. This also indicates a shifting thermal centroid

between the lesion body at earlier times due to enhanced restored crystallinity and at later

periods when the surface layer build up shifts the thermal centroid toward the surface.

Restoration of subsurface lesion crystallinity during earlier remineralization times would

improve the thermal properties of the lesion body, providing a better conduction medium for

thermal propagation and as a result a greater amount of thermal energy will be transmitted

through the enamel section. As sound enamel prisms may act as optical waveguides of the

incident laser light (Odor et al. 1996), enhanced subsurface crystallinity would restore optical

paths and improve light propagation and transmission. However, enhanced remineralization

within the porous demineralized lesion body is likely to occur with a concomitant deposition at

the enamel surface. According to the abovementioned interplay mechanisms, when subsurface

remineralization is dominant over surface mineral deposition, an amplitude increase occurs with

a phase lag decrease, as the quantity of transmitted energy increases. However, when mineral

deposition becomes dominant within the intact surface layer such that the increase in mineral

volume creates a diffusion barrier for mineral ion flux deeper into the lesion and/or the thermal

mismatch between the surface layer and deeper layers becomes large, the thermal centroid shifts

in the opposite direction and the transmitted signal intensity decreases. It may also be possible

that once the surface layer reaches a critical thickness, its properties become dominant at the

expense of the deeper layers. Transmission-LUM signals did not exhibit the same sensitivity

upon remineralization as did PTR. This is likely related to the fact that the LUM signal channel

is not depth-selective. Insensitivity of the LUM signal channel to depth-dependent processes

107

occurs as higher lesion scattering coefficients will scatter the initial laser radiation as well as

scatter the LUM photons, preventing the photons from transmitting through the enamel section.

However, better contrast was observed in backscatter LUM signals, as processes were monitored

from the sample surface through the remineralizing solution. A large increase in backscatter

LUM following remineralization may be due to restoration of surface crystallinity. This increase

was transient, and after ≈200 hrs began to decrease over time. The decrease in the LUM at later

treatment times is consistent with the increase in scattering coefficient noted in chapter 1, at

prolonged remineralization times, and is also consistent with the observed transient PTR signal

changes as scattering coefficients have a significant influence on thermal centroid localization

within enamel. A less marked decrease in phase lag and increase in amplitude may be a result of

the large demineralized lesion body that persisted following remineralization. The lack of

remineralization within the lesion body of the sample presented in Fig. 2.6 may be explained by

the extremely low mineral volume of the lesion body. With a mineral volume level around 20 -

30 vol%, complete dissolution of subsurface enamel crystallites may occur. As a result, upon

remineralization, fewer partially demineralized crystallites are available as scaffolds for mineral

reprecipitation and growth. In this case, de novo mineral precipitation is the mechanism required

for restoring the demineralized lesion, which requires larger driving forces for remineralization

within the lesion body. As the hypomineralized surface layer would maintain partially

demineralized crystallites, it would therefore be expected that remineralization of the surface

layer be the dominant mechanism, which was demonstrated in the increase in back-scatter LUM

signal at earlier remineralization times.

9.3 Errors and limitations of transmission PTR-LUM measurements

A possible source of error in the transmission measurements may be due to the presence of the

treatment solutions. The influence of the demineralizing gel and remineralizing solution on PTR

and LUM signal generation are shown in Appendix 5 (Figs. A.5.2 - A.5.4). Since the

demineralizing gel is slightly yellow in colour, its mere presence will induce a slight increase in

absorption and as a result, reduce the laser intensity delivered to the enamel surface (Fig. A.5.3).

However, regardless of the initial effects of the treatment solutions, the relative signal channels,

which were monitored in the present study, would not be affected. Furthermore, during

demineralization when the concentration of out-diffused mineral ions accumulates in the gel

108

layer surrounding enamel, a cloudy and diffuse accretion of particles is evident and showed a

slight influence on PTR (1 Hz) and LUM (89 Hz) at the probed frequencies (Fig. A.5.4). As

slight absorption was noted in the presence of the demineralizing gel (Fig. A.5.3), the switch

from the yellowish demineralizing medium to the transparent remineralizing medium induced

additional minor changes at 1 Hz (Fig. A.5.2) that may alter the laser energy distributed at the

surface of the enamel section.

9.4 Future directions

Future directions in the analysis of transmission measurements will include the application of a

modified 2-layer theoretical model to the PTR data. This will allow for the extraction of opto-

thermophysical parameters and the change in these parameters can be evaluated over time.

Quantifying the formation and regression of layer thicknesses in thin enamel sections may be

essential in determining the effectiveness of various demineralizing agents in producing

reproducible substrates for remineralization studies, as well as efficacy of remineralizing agents,

topical solutions and/or artificial saliva analogues. This study has shown that LUM can be used

for back-propagation interface studies and this channel is more sensitive than transmission LUM.

Furthermore, PTR, even in transmission mode, is very sensitive to front surface demineralization

and remineralization processes.

109

10 Significance

The results of the present study were generated in a highly-controlled environment which is

clearly not the situation in vivo. A likely factor expected to limit the potential application of the

photothermal radiometric technique to clinical settings is the presence of saliva. Saliva is 99.9%

by composition water and as depicted in Fig. 7 it has a strong absorption band in the mid IR.

Therefore, the collection of IR emissions through a water based solution would be significantly

attenuated, as was observed in the real-time PTR-LUM experiment. PTR was unable to monitor

changes in real-time as the demineralizing and remineralizing solutions were predominately

water-based. However, modulated LUM would not be plagued by strong water absorption bands

as the spectral range of the emitted luminescence (≈750 - 830-nm) peaks at a smaller wavelength

where water absorption is minimal. Nevertheless, modulated LUM, as an optical phenomenon is

highly sensitive to light scattering processes which change based on the hydration level of the

tooth, as seen earlier, and as all other optical techniques, such as QLF and DIAGNOdent would

be affected by the presence of stains and plaque (Angmar-Månsson et al. 2000). The presence of

plaque can be easily overcome by debriding the tooth surfaces prior to measurements. While the

overall magnitude of the PTR amplitude may be altered by the presence of stain and plaque, PTR

phase has established itself as the more sensitive channel due to its relative insensitivity to

surface features, which highlights the significant advantage of the multi-channel PTR technique.

A laser fluorescence (DIAGNOdent) study found a significant influence of in vitro storage

conditions and tooth hydration level on the fluorescence response (Francescut et al. 2006). These

same challenges of hydration have been confronted by other caries technologies such as QLF

(Pretty et al. 2004) and electrical conductance measurements (Ricketts et al. 1997). In order to

overcome the influence of hydration on the generated PTR-LUM signals, a reliable and clinically

reproducible drying technique is required for maintaining stable conditions for longitudinal

monitoring. This may include cotton roll isolation and/or chair-side compressed air for quick

drying of the samples, the rate of which is affected by room temperature and individual humidity

levels. In terms of QLF measurements, compressed air was found to be the most effective and

expeditious dehydration method for reproducible measurements over time. A drying time of 15

seconds was found to be sufficient for the abovementioned QLF measurements, which is an

110

established and clinically reasonable drying period (Pretty et al. 2006). A critical future test of

the PTR-LUM system must identify and evaluate the efficacy of a standardized drying technique

in vivo, which is vital in order to minimize errors and prove the device reliability toward the

future clinical application of the device. An additional limitation in the present study was that

caries was simulated without bacterial involvement and at room temperature. The collected

thermal signal should not be affected by physiological temperatures within the oral cavity as the

use of lock-in detection operates by locking onto the phase of the source frequency and therefore

removing all other component frequencies. As noted above, the phase signal channel is relatively

insensitive to such variations, while the overall PTR amplitude signal may change under

different temperature and hydration conditions.

The lesions created in the present study, using the acidified gel system, were small in size (mean

depth = 90 μm) (Table 10). A clinical diagnosis based on the detection of such small lesions less

than 100 µm would most likely involve patient education in optimizing plaque control and

salivary flow as well as decreasing the intake frequency of fermentable carbohydrates in order to

favour lesion repair without clinician intervention (Murdoch-Kinch and McLean 2003).

Monitoring these incipient lesions over time will ultimately determine whether the lesion

progresses to the point where therapeutic agents such as topical fluorides might be encouraged to

reverse the non-cavitated lesion or to the point of cavitation where restorative intervention is

necessary. Furthermore, this emphasizes the distinction between detection and diagnosis where

the former is only one component of a clinician‘s arsenal in deciding the overall diagnosis and

treatment option.

A substantial limitation in the application of the PTR-LUM system in the present study is the

restriction of the quantification of simulated caries to smooth surfaces, given that the majority of

caries lesions are presently found on occlusal and approximal tooth surfaces. Nevertheless, this

study is vital in the advancement of quantitative, non-destructive evaluation of the caries process.

As enamel and dentin are turbid media, with complicated structural geometries varying as a

function of depth it is important to start out with the simplest approximation of reality, in this

case, smooth surfaces, which maintain a relatively flat geometry with near-one-dimensional

diffusion processes during lesion formation. Only after gaining a complete understanding of the

111

PTR-LUM signals and combined theoretical formalism to the general cases, can one progress to

more complicated geometries and clinically relevant case studies such as intricate occlusal

fissures or approximal surfaces. The transmission-mode PTR-LUM sensitivity to simulated

caries in thin enamel sections, however, may prove efficacious in detecting and monitoring the

caries process at approximal contact points where the thinnest enamel layer can be found with no

dentinal involvement. The merits of a non-destructive early detection system relate to the

avoidance of high levels of damaging ionizing radiation as well as the detection of caries in tooth

surfaces not readily visible, such as hidden caries in the occlusal fissures and approximal

surfaces, where the caries incidence is high and current radiographic detection methods suffer.

The most feasible methods of clinically assessing caries progression, at present, are bitewing

radiographs combined with visual and/or tactile sensation (Benn 1994; Angmar-Månsson and ten

Bosch 1993). However, considering both the sensitivity and specificity of bitewing radiographs

in the detection of approximal caries lesions, 0.66 and 0.95, respectively, and the sensitivity and

specificity of visual-tactile examination for the same lesions, 0.52 and 0.98, respectively, poor

sensitivity for such lesions is clearly evident (Bader et al. 2001; Baelum 2010). In terms of

occlusal caries, the sensitivities of radiographic and visual-tactile examination are also poor at

≈30% and ≈18%, respectively (Bader et al. 2001). Thus, there is a strong driving force toward

the development of a sensitive caries detection technique and instrumentation applicable to

challenging assessment regions and provide additional quantitative information in the

augmentation of the disease characterization process. Although there have been numerous caries

detection systems investigated in vitro and evaluated clinically, at present, there is no single

detection system capable of reliably detecting caries on all tooth surfaces (Ferriera Zandona and

Zero 2006).

Several advantages and applications from the present study and in the development of a non-

invasive quantitative caries detection system which includes patient education in allowing the

longitudinal monitoring of caries activity without exposure to ionizing radiation, the specific

tailoring of remineralization therapies to the individual level, assessment of lesion activity in

order to distinguish active vs. arrested lesions, detailed in vitro, in situ and/or in vivo

investigations of de- and remineralization mechanisms without sample interruption and

destruction, and lastly the assessment of the efficacy of various remineralization agents for

112

clinical trials. In terms of the latter, continuous monitoring of enamel sections in transmission-

mode PTR-LUM without sample disruption would be ideal to establish effectiveness of topical

solutions, pastes, varnishes or rinses. In addition, future studies may consider modifying the

transmission-mode PTR-LUM experimental setup in order to include continuous flow chambers

analogous to in vitro artificial mouth setups in order to more closely simulate demineralization

and remineralization process occurring in vivo. It may be likely, sometime in the near future, that

direct quantitative information will be obtained through simple chair-side measurements in such

a manner that sound enamel and enamel caries structural geometry as a function of depth can be

reconstructed. Furthermore, this may provide insight into lesion activity, i.e. discerning between

active and arrested lesions, which may assist in tailoring remineralization therapies toward active

lesions and preventing unnecessary overtreatment of the arrested-type.

113

11 Summary

As a non-destructive technique, the combination of PTR and LUM along with the theoretical

model provides 4 distinct signal channels along with a comprehensive theoretical formalism to

yield quantitative information regarding lesion severity and the change in severity over time.

Although the results of the present study cannot be directly extrapolated to clinical environments,

it undoubtedly advances the discipline of quantitative dental diagnostics and forms the widest

parameter basis for future research in the field. Furthermore, quantitative extraction of optical

and thermal properties from intact, whole teeth, rather than prepared thin sections, allows for the

investigation of opto-thermophysical parameters under conditions more reflective of the natural

oral environment. The promising results from the present investigation places the quantitative

PTR and LUM technique at the forefront of non-destructive caries evaluation in vitro, above

existing purely optical systems, in terms of the total information extracted from the generated

signals. In light of the results of the present study the hypothesis is accepted in that the combined

detection modes of PTR-LUM proved to be efficacious in measuring and quantifying

mineralized layers generated during de- and remineralization processes.

12 Conclusions

From the combined backscatter and transmission-mode PTR-LUM experiments the following

conclusions could be drawn:

1. PTR and LUM signals in backscatter-mode were effective in detecting and monitoring

the formation, progression and regression of simulated enamel demineralized and

remineralized lesions. The complementary nature of the PTR trends under 830-nm as

observed under 660-nm laser radiation, illustrates the dual-effectiveness of either laser

wavelength in detecting incipient demineralized and remineralized enamel lesions.

2. The theoretical formalism developed to explain PTR signal trends proved to be effective,

reliable and reproducible in characterizing opto-thermophysical parameters of sound

enamel.

114

3. The high fidelity of the developed theoretical/computational model illustrates its

effectiveness and applicability to non-destructively quantify lesion thicknesses and

reconstruct opto-thermophysical parameters as a function of depth. Furthermore, the

fitting procedure implemented in this work, increased the robustness of the computational

algorithm, providing a unique solution for the multiparameter fits of multi-layered sound

enamel and enamel caries lesions.

4. Real-time acquisition of PTR and LUM signals in transmission-mode proved effective in

detecting and monitoring simulated demineralized and remineralized lesions in thin

enamel sections. Modulated LUM in backscatter was also sensitive in monitoring lesion

progression without sample disruption in the treatment solutions.

5. From both experiments it is clear that remineralization entails a multi-factorial and

complex process involving the interplay between shifting thermal centroids as mineral

gains in surface and subsurface regions alter the opto-thermophysical properties of the

effective layers. The theoretical model pointed to enhanced effectiveness of subsurface

lesion remineralization in the presence of fluoride, however, no statistically significant

differences in TMR defined mineral loss and lesion depth were noted between the

remineralization treatment groups.

115

13 Appendices

13.1 Appendix 1

13.1.1 PTR frequency response (830-nm laser)

Trends in the amplitude and phase frequency response under the 830-nm laser were similar to

those detailed for the smaller wavelength light (660-nm). Amplitude and phase for the 10-day

and 40-day demineralized samples are shown in Fig. A.1.1. Amplitude ratios and phase

differences, normalized with respect to the final demineralization curve, of the exemplary

samples from the fluoride-free, low fluoride and high fluoride group are presented in Figs. A.1.2

- A.1.4. Overall, similar trends were evident between the 2 wavelengths investigated. However,

trends in the phase behaviour under the 830-nm laser were difficult to discern, across the entire

modulation frequency range, due to the poorer SNR of the longer wavelength light.

Figure A.1.1. PTR amplitude and phase curves under the 830-nm laser for (A) the 10-day

demineralized sample and (B) the 40-day demineralized sample. The corresponding

116

microradiographs and mineral content depth profiles for (A) and (B) are presented in Fig. 16 and

Fig. 17, respectively. Error bars, when not visible, are of the size of the symbols.

Figure A.1.2.PTR amplitude ratio and phase difference with respect to the final demineralization

state for a sample in the fluoride-free treatment group under 830-nm laser excitation.

Corresponding microradiograph and mineral volume profile are shown in the adjacent figures.

Error bars, when not visible, are of the size of the symbols.

1 10 100 1000

1.2

1.4

1.6

1.8

2.0

2.2

Remin- 2 Days

Remin- 5 Days

Remin- 10 Days

Remin- 20 Days

Remin- 28 Days

Am

plit

ude R

atio (

V/V

0)

Frequency (Hz)

1 10 100 1000

-9

-6

-3

0

3

6

9

12

PTR Amplitude

PTR Phase

Phase D

iffe

rence ( -

0)

Frequency (Hz)

1 10 100 1000

1.2

1.4

1.6

1.8

2.0

2.2

Remin- 2 Days

Remin- 5 Days

Remin- 10 Days

Remin- 20 Days

Remin- 28 Days

Am

plit

ude R

atio (

V/V

0)

Frequency (Hz)

1 10 100 1000

-9

-6

-3

0

3

6

9

12

PTR Amplitude

PTR Phase

Phase D

iffe

rence ()

Frequency (Hz)

100 µm

117

Figure A.1.3. PTR amplitude ratio and phase difference with respect to the final

demineralization state for a sample in the low fluoride (1 ppm) treatment group, under 830-nm

laser excitation. Corresponding microradiograph and mineral volume profile are shown in the

adjacent figures. Error bars, when not visible, are of the size of the symbols.

1 10 100 1000

1.1

1.2

1.3

1.4

1.5

1.6

Remin- 2 Days

Remin- 5 Days

Remin- 10 Days

Remin- 20 Days

Remin- 28 DaysA

mplit

ude R

atio (

V/V

)

Frequency (Hz)

1 10 100 1000

-6

-4

-2

0

2

4

6

8

PTR Amplitude

PTR Phase

Phase D

iffe

rence ( -

)

Frequency (Hz)

1 10 100 1000

1.1

1.2

1.3

1.4

1.5

1.6

Remin- 2 Days

Remin- 5 Days

Remin- 10 Days

Remin- 20 Days

Remin- 28 Days

Am

plit

ude R

atio (

V/V

0)

Frequency (Hz)

1 10 100 1000

-4

-2

0

2

4

6

8

PTR Amplitude

PTR Phase

Phase D

iffe

rence (-

0)

Frequency (Hz)

100 µm

118

Figure A.1.4. PTR amplitude ratio and phase differences with respect to the final

demineralization state for a sample in the high fluoride (1000 ppm) treatment group, under 830-

nm laser excitation. Corresponding microradiograph and mineral volume profile are shown in the

adjacent figures. Error bars, when not visible, are of the size of the symbols.

1 10 100 1000

1.0

1.5

2.0

Am

plit

ude R

atio (

V/V

0)

Frequency (Hz)

1 10 100 1000

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

14

Remin- 2 Days

Remin- 5 Days

Remin- 10 Days

Remin- 20 Days

Remin- 28 Days

PTR Amplitude

PTR PhasePhase D

iffe

rence (-

0)

Frequency (Hz)

100 µm

1 10 100 1000

1.0

1.2

1.4

1.6

1.8

2.0

2.2

Am

plit

ude R

atio (

V/V

0)

Frequency (Hz)

1 10 100 1000

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

14

Remin- 2 Days

Remin- 5 Days

Remin- 10 Days

Remin- 20 Days

Remin- 28 Days

PTR Amplitude

PTR Phase

Phase D

iffe

rence (-

0)

Frequency (Hz)

119

13.2 Appendix 2

The following figures present the theoretical fits of sound (Fig. A.2.1) demineralized (A.2.2a-d)

and remineralized enamel (Figs. A.2.3 – A.2.5) superposed on the experimental data. In all cases,

a good fit between theoretical curves and experimental data points was observed. From the

theoretical fitting curves to experimental data, opto-thermophysical depth profiles for multi-

layered enamel were reconstructed.

Figure A.2.1. Multi-parameter fitting of amplitude and phase curves of a sound tooth.

Experimental data are represented by symbols (*). Calculated theory is shown as solid lines.

101

102

10-1

100

Frequency (Hz)

PTR

Am

plit

ud

e (a

.u.)

101

102

-85

-80

-75

-70

-65

Frequency (Hz)

PTR

ph

ase,

deg

120

Figure A.2.2. PTR amplitude and phase experimental and 3-layer theory plots for the (a) 10-day

demineralized sample and (b) the 40-day demineralized sample. Experimental data are

represented by symbols and calculated theory is shown as solid lines.

101

102

-100

-90

-80

-70

-60

Frequency (Hz)

PTR

pha

se, d

eg

Sound enamel

Demin-5day

Demin-10day

101

102

10-2

10-1

100

101

Frequency (Hz)

PTR

Am

plit

ude

(a.u

.)

Sound enamel

Demin-5day

Demin-10day

(A)

101

102

-75

-70

-65

-60

-55

Frequency (Hz)

PTR

ph

ase,

deg

Sound enamel

Demin-5day

Demin-10day

Demin-15day

Demin-20day

Demin-30day

Demin-40day

101

102

10-1

100

Frequency (Hz)

PTR

Am

plit

ud

e (a

.u.)

Sound enamel

Demin-5day

Demin-10day

Demin-15day

Demin-20day

Demin-30day

Demin-40day

(B)

121

Figure A.2.3. PTR amplitude and phase experimental and 3-layer theory plots for the fluoride-

free sample. Experimental data are represented by symbols and calculated theory is shown as

solid lines.

Figure A.2.4. PTR amplitude and phase experimental and 3-layer theory plots for the low

fluoride sample. Experimental data are represented by symbols and calculated theory is shown as

solid lines.

101

102

10-1

100

Frequency (Hz)

P

TR A

mp

litu

de

(a.u

.)

Demin-10day

Remin-2day

Remin-5day

Remin-10day

Remin-20day

Remin-28day

101

102

-70

-68

-66

-64

-62

-60

Frequency (Hz)

PTR

ph

ase,

deg

Demin-10day

Remin-2day

Remin-5day

Remin-10day

Remin-20day

Remin-28day

101

102

10-1

100

Frequency (Hz)

PTR

Am

plit

ud

e (a

.u.)

Demin-10day

Remin-2day

Remin-5day

Remin-10day

Remin-20day

Remin-28day

101

102

-70

-68

-66

-64

-62

Frequency (Hz)

PTR

ph

ase,

deg

Demin-10day

Remin-2day

Remin-5day

Remin-10day

Remin-20day

Remin-28day

122

Figure A.2.5. PTR amplitude and phase experimental and 3-layer theory plots for the high

fluoride group. Experimental data are represented by symbols and calculated theory is shown as

solid lines.

101

102

10-1

100

Frequency (Hz)

PTR

Am

plit

ud

e (a

.u.)

Demin-10day

Remin-2day

Remin-5day

Remin-10day

Remin-20day

Remin-28day

101

102

-80

-75

-70

-65

Frequency (Hz)

PTR

ph

ase,

deg

Demin-10day

Remin-2day

Remin-5day

Remin-10day

Remin-20day

Remin-28day

123

13.3 Appendix 3

13.3.1 Additional optothermal parameters

The following section presents the auxiliary parameters derived from the theoretical fitting

program outlined in Table 6 and not described in detail within the text. These parameters

include: the cosine of the scattering angle (g), the infrared absorption coefficient (μIR), the optical

reflection coefficients from the L1-L2 boundary (R2) and L2-L3 boundary (R3) and lastly the non-

radiative energy conversion efficiency within each layer (ηNR).

Supplementary optothermal depth profiles for the 10-day demineralized sample and the 40-day

demineralized are shown in Figs. A.3.1 and A.3.2, respectively. In addition, the auxiliary

parameters from the samples in the fluoride-free (Fig. A.3.3), low fluoride (Fig. A.3.4) and high

fluoride group (Fig. A.3.5) are shown.

Figure A.3.1. The change in optothermal parameters as a function of time for the 10-day

demineralized sample. (a) Scattering anisotropy, (b) IR absorption coefficient, (c) Reflection

coefficients and (d) Non-radiative efficiency, are presented for each layer over the

demineralization period. Layer 1 = surface layer; Layer 2 = lesion body.

0 5 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Co

s Sc

atte

rin

g A

ngl

e (

g)

Treatment Time (days)

Layer 1

Layer 2

0 5 10

60000

80000

100000

120000

140000

160000

180000

200000

IR A

bso

rpti

on

Co

eff

icie

nt

(m-1

)

Treatment Time (days)

0 5 10

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Re

fle

ctio

n C

oe

ffic

ien

t (R

)

Treatment Time (days)

R2

R3

0 5 10

30

40

50

60

70

80

90

No

n-R

adia

tive

Eff

icie

ncy

(%

)

Treatment Time (days)

Layer 1

Layer 2

(b)(a)

(d)(c)

124

Figure A.3.2. The change in optothermal parameters as a function of time for the 40-day

demineralized sample. (a) Scattering anisotropy, (b) IR absorption coefficient, (c) Reflection

coefficients and (d) Non-radiative efficiency, are presented for each layer over the

demineralization period. Layer 1 = surface layer; Layer 2 = lesion body.

0 10 20 30 40

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Co

s Sc

atte

rin

g A

ngl

e (g

)

Treatment Time (days)

Layer 1

Layer 2

0 10 20 30 4050000

75000

100000

125000

150000

175000

IR A

bso

rpti

on

Co

eff

icie

nt

(m-1

)

Treatment Time (days)

0 10 20 30 40

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Re

fle

ctio

n C

oe

ffic

ien

t (R

)

Treatment Time (days)

R2

R3

0 10 20 30 400

10

20

30

40

50

60

No

n-R

adia

tive

Eff

icie

ncy

(%

)

Treatment Time (days)

Layer 1

Layer 2

(b)(a)

(d)(c)

125

Figure A.3.3. The change in optothermal parameters as a function of time for the fluoride-free

sample. (a) Scattering anisotropy, (b) IR absorption coefficient, (c) Reflection coefficients and

(d) Non-radiative efficiency, are presented for each layer over the de- and remineralization

periods. Layer 1 = surface layer; Layer 2 = lesion body.

0 10 20 30 40

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

ReminDemin

Co

s Sc

atte

rin

g A

ngl

e (g

)

Treatment Time (days)

Layer 1

Layer 2

0 10 20 30 4020000

30000

40000

50000

60000

70000

80000

90000

100000

110000

ReminDemin

IR A

bso

rpti

on

Co

eff

icie

nt

(m-1

)

Treatment Time (days)

0 10 20 30 40

0.0

0.2

0.4

0.6

0.8

1.0

ReminDemin

Ref

lect

ion

Co

effi

cien

t (R

)

Treatment Time (days)

R2

R3

0 10 20 30 400

10

20

30

40

50

60

70

80

ReminDemin

No

n-R

adia

tive

Eff

icie

ncy

(%

)

Treatment Time (days)

Layer 1

Layer 2

(b)

(d)(c)

(a)

126

Figure A.3.4. The change in optothermal parameters as a function of time for the low fluoride

sample. (a) Scattering anisotropy, (b) IR absorption coefficient, (c) Reflection coefficients and

(d) Non-radiative efficiency, are presented for each layer over the de- and remineralization

periods. Layer 1 = surface layer; Layer 2 = lesion body.

0 10 20 30 40

0.3

0.4

0.5

0.6

0.7

0.8

0.9

ReminDeminCo

s Sc

atte

rin

g A

ngl

e(g)

Treatment Time (days)

Layer 1

Layer 2

0 10 20 30 4060000

80000

100000

120000

140000

160000

180000

200000Demin Remin

IR A

bso

rpti

on

Co

eff

icie

nt

(m-1

)

Treatment Time (days)

0 10 20 30 40

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

ReminDemin

Ref

lect

ion

Co

effi

cien

t (R

)

Treatment Time (days)

R2

R3

0 10 20 30 40

10

20

30

40

50

60

70

80

ReminDemin

No

n-R

adia

tive

Eff

icie

ncy

(%

)

Treatment Time (days)

Layer 1

Layer 2

(b)

(d)(c)

(a)

127

Figure A.3.5. The change in optothermal parameters as a function of time for the high fluoride

sample. (a) Scattering anisotropy, (b) IR absorption coefficient, (c) Reflection coefficients and

(d) Non-radiative efficiency, are presented for each layer over the de- and remineralization

periods. Layer 1 = surface layer; Layer 2 = lesion body.

0 10 20 30 40

0.2

0.4

0.6

0.8

1.0

ReminDeminCo

s Sc

atte

rin

g A

ngl

e (g

)

Treatment Time (days)

Layer 1

Layer 2

0 10 20 30 40

20000

40000

60000

80000

100000

120000

140000

160000

180000

200000Demin Remin

IR A

bso

rpti

on

Co

eff

icie

nt

(m-1

)

Treatment Time (days)

0 10 20 30 40

0.0

0.2

0.4

0.6

0.8

1.0

Remin

Demin

Re

fle

ctio

n C

oe

ffic

ien

t (R

)

Treatment Time (days)

R2

R3

0 10 20 30 40

10

20

30

40

50

60

70

80

90

ReminDeminNo

n-R

adia

tive

Eff

icie

ncy

(%

)

Treatment Time (days)

Layer 1

Layer 2

(b)

(d)(c)

(a)

128

13.4 Appendix 4

The following section presents an assessment of the error in experimental data on the theoretical

derivation of optical and thermophysical parameters. In the first test, 3 individual fits were

performed and compared in order to evaluate sources of error from experimental data. The first

fit involved the experimental raw PTR amplitude and phase data to generate a set of opto-

thermophysical parameters. In the second and third fits, the maximum and minimum PTR

amplitude and phase ranges were determined by adding and subtracting experimental standard

deviations from the averaged PTR signals, respectively (Fig. A.4.1). The percentage difference

was then calculated between the resultant parameters derived from the first fit and the average of

the minimum and maximum range in order to assess the deviation in parameter as a function of

the standard deviation of the PTR measurements (Table A.4.1).

Figure A.4.1. The influence of PTR raw data standard deviation on the outcome of theoretical

fitting. Error max and Error min refer to PTR amplitude and phase signals plus and minus

standard deviation, respectively. Experimental data are represented by symbols and calculated

theory is shown by solid or dotted lines.

A good agreement between the averaged PTR data and the average PTRmax and PTRmin can be

seen. This illustrates that large error bars in the PTR raw data measurement can have a

significant influence on the generated set of opto-thermophysical parameters, however,

differences were mainly seen in the optical properties and less so in the thermal properties and

thickness values. Therefore, for future applications of the theoretical algorithm it is important to

maximize the SNR of the experimental data and/or fit the raw data to a polynomial function in

101

102

100

Frequency (Hz)

PT

R A

mp

litu

de

(a

.u.)

3-L Theory- Error MIN

3-L Theory- Error MAX

Experimental- Error MIN

Experimental- Error MAX

101

102

-72

-70

-68

-66

-64

-62

Frequency (Hz)

PT

R P

ha

se

(d

eg

)

3-L Theory- Error MIN

3-L Theory- Error MAX

Experimental- Error MIN

Experimental- Error MAX

129

order to attain a smooth curve for the fitting procedure, as extraneous data points can add

significant deviation in the generated parameters. Adhering to these guidelines would

significantly reduce the overall calculation time of the theoretical algorithm, which at present is

the time-limiting factor, and augment the validity of the derived parameters.

Table A.4.1. Percentage difference attributed to the standard deviation of experimental PTR

measurements.

The results of a second test on the validity of the computational algorithm are presented in Table

A.4.2. In this test the PTR curves from frequency scans at the final treatment point were fitted

with ‗open‘ and ‗closed‘ thickness limits. Closed thickness limits refer to the fitting procedure

outlined in Fig. 13 and described in detail in sub-section 1.7 of chapter 1. This involved fitting

the final PTR treatment curve based on the maximum and minimum thicknesses determined

from the TMR mineral content depth profiles. The closed limits refer to the situation where the

final thicknesses are known values. Open thickness limits refers to the situation where it is

assumed that the final thicknesses are unknown values. The limits that were defined for layer 1

and layer 2 for the ‗open‘ fit were determined from the minimum and maximum range of

thicknesses for the surface layer and lesion body from all TMR mineral content profiles in the

study. The results of this satellite experiment demonstrated large variation in the generated

optical properties, while less deviation was noted for the thermal properties. Most importantly,

the thickness values showed great convergence to more or less the same values. This indicates

that layer thicknesses could be predicted within ≈20% error which strengthens the overall power

and legitimacy of the derived theoretical formalism in non-destructively quantifying layer

Parameters PTR Amp and phase + S.D.

(PTRMax)

PTR Amp and phase – S.D.

(PTRMIN)

Average (PTRMax) and

(PTRMIN)

Fitted PTR average

Percent difference

(%)

µa1 114 104 109 141 26

µa2 22 51 37 43 16

µs1 151156 105971 128564 117427 9

µs2 100530 144472 122501 144369 16

κ1 0.76 0.35 0.56 0.53 5

κ2 0.45 0.48 0.47 0.45 3

α1 7.1 x 10-7 6.2 x 10-7 6.7 x 10-7 7.3 x 10-7 9

α2 2.5 x 10-7 2.8 x 10-7 2.7 x 10-7 2.5 x 10-7 6

L1 20.2 14.0 17.1 18.7 9

L2 79.8 93.1 86.5 92.1 6

130

thicknesses. The fact that the ‗open‘ thickness values converged to more or the same values as

the ‗closed‘ is an important finding, since the former situation may occur clinically where the

thicknesses are clearly unknown.

Table A.4.2. The percent differences for fitting the final demineralized and final remineralized

PTR curves with open thickness limits (DOPEN and ROPEN) and closed thickness limits (DLIMIT and

RLIMIT). D and R refer to demineralized and remineralized, respectively. For an explanation of

‗open‘ and ‗closed‘ limits see text body. Subscript numbers refer to the layer, where 1 is the

intact surface layer (layer 1) and 2 is the lesion body (layer 2).

Parameters DLIMIT DOPEN Percent

difference (%)

RLIMIT ROPEN Percent

difference (%)

µa1 141 78 58 141 36 118

µa2 43 40 7 40 31 24

µs1 117427 134711 14 226 210 69

µs2 144369 111874 25 149920 58982 87

κ1 0.53 0.37 35 0.68 0.76 11

κ2 0.45 0.53 17 0.43 0.44 1

α1 7.3 x 10-7 6.8 x 10-7 7 6.7 x 10-7 6.4 x 10-7 4

α2 2.5 x 10-7 3.0 x 10-7 18 2.2 x 10-7 2.1 x 10-7 4

L1 18.7 18.7 0 15.1 12.1 22

L2 92.1 102.1 10 39.7 39.3 1

131

13.5 Appendix 5

13.5.1 The effect of incubation in the humid chamber on backscatter PTR-LUM

signals

At the end of each designated treatment period, individual samples were removed from their

treatment solutions, washed, dried and placed in a thermodynamic chamber overnight before

PTR-LUM measurements were executed. In order to examine the effects of PTR-LUM signal

drift due to changes in humidity over time of exposure inside the humid chamber, the following

satellite measurement was performed. A sound enamel sample was scanned at day 0 and after 2

and 4 days of incubation inside the humid chamber. Prior to each measurement the sample was

removed from the chamber, allowed to dry in the air for 40 min, followed by a further 20 min

under direct laser radiation for thermal stabilization purposes. From the results presented in Fig.

A.5.1, it is apparent that incubation in the humid box overnight or over a weekend did not

significantly affect PTR signal generation. On the other hand, LUM after 2 days also did not

exhibit any change in signal however, after 4 days there was slight decrease in amplitude and

small scale changes in phase. Thus, small changes in LUM signals may be influenced by sample

hydration levels over time rather than signal being solely dependent on individual treatments,

consistent with recent PTR-LUM studies (Jeon et al. 2007, 2008).

132

Figure A.5.1. The effect of incubation time in the humidity chamber on PTR - LUM signals.

13.5.2 The effect of the treatment solutions on transmission-mode

PTR-LUM

Using a thin sheet of aluminum foil in place of enamel section, frequency scans were performed

before and immediately following the addition of the acid gel medium to the treatment container.

After gel was decanted, PTR amplitude decreased with a marked behaviour at low modulation

frequencies and PTR phase lag decreased with enhanced phase curvature in the low modulation

frequency range (Fig. A.5.2a). Frequency scans following the replacement of the

demineralization gel with the remineralizing solution are shown in Fig. A.5.2b. A switch from

the demineralizing to remineralizing solution produced a slight decrease in amplitude across the

1 10 100 1000

1E-4

1E-3

0.01

Am

plit

ude (

a.u

.)

Frequency (Hz)1 10 100 1000

0.12

0.14

0.16

0.18

0.20

0.22PTR Amplitude LUM Amplitude

Am

plit

ude (

a.u

.)

Frequency (Hz)

1 10 100 1000

-90

-85

-80

-75

-70

-65 PTR Phase

Phase (

Deg)

Frequency (Hz)1 10 100 1000

-18

-16

-14

-12

-10

-8

-6

-4

-2

Humid Box- Day 0

Humid Box- Day 2

Humid Box- Day 4

LUM phase

Phase (

Deg)

Frequency (Hz)

133

entire modulation frequency range. PTR phase of the remineralizing solution curve converged to

the same values of the demineralization gel curve, apart from a small decrease in phase lag at 1 –

2 Hz.

Figure A.5.2. Transmission-mode PTR frequency response of an aluminum foil sample

illustrating the effect of demineralization gel (a) and demineralizing and remineralizing solutions

(b) on signal generation.

The same experiment as detailed above using the demineralization gel was performed with an

enamel section and is shown in Fig. A.5.3. After the addition of the demineralization gel, PTR

amplitude decreased very slightly across the entire modulation frequency range. PTR phase

showed no effect at frequencies above 4 Hz. At 1 Hz, PTR phase lag decreased whereas an

134

increase in phase lag was observed at 2 - 3 Hz. A large decrease in both LUM amplitude and

phase was noted after gel was added.

Figure A.5.3. Transmission-mode PTR-LUM signals with an enamel section under empty

treatment container and demineralization gel filled container conditions.

Following all demineralization treatments, the accumulation of out-diffused mineral and organic

factions from the treated enamel section sated the demineralizing gel media. The effect of PTR-

LUM signal generation in the particle-laden used demineralization gel vs. fresh particulate-free

gel was tested and shown in Fig. A.5.4. After the replacement of the undisturbed, used gel with

fresh medium, PTR amplitude slightly increased across the entire modulation frequency range

with a concomitant small decrease in phase lag at 1 - 3 Hz with minimal change in the phase

frequency response at frequencies greater than 3 Hz. A comparable increase in LUM amplitude

1 10 100

1E-4

1E-3

0.01

Am

plit

ude (

a.u

.)

Frequency (Hz)1 10 100 1000

0.30

0.35

0.40

0.45

0.50

0.55

Empty Container

Gel - filled Container

PTR Amplitude LUM Amplitude

Am

plit

ude (

a.u

.)Frequency (Hz)

1 10 100

-120

-115

-110

-105

-100

-95

-90

-85

-80

PTR Phase

Phase (

Deg)

Frequency (Hz)1 10 100 1000

-14

-12

-10

-8

-6

-4

-2

LUM phase

Phase (

Deg)

Frequency (Hz)

135

was also noted with a slight increase in phase minimum. As the incident radiation must

propagate through the demineralizing and remineralizing media to reach the tooth surface, the

presence of significant scatters within the bulk media can significantly affect the amount of laser

energy deposited inside the tooth, as evidenced from the change in PTR-LUM signals with the

fresh vs. used demineralizing gel. Thus, particulates within the demineralizing medium cannot be

ruled out as a source of signal generation in transmission measurements as small contributions to

PTR-LUM signals are noted.

Figure A.5.4. The effect of new and used demineralization gel on transmission-mode PTR-LUM

signal generation.

1 10 100 1000

1E-4

1E-3

0.01

Am

plit

ude (

a.u

.)

Frequency (Hz)1 10 100 1000

0.18

0.24

0.30

PTR Amplitude LUM Amplitude

Am

plit

ude (

a.u

.)

Frequency (Hz)

1 10 100 1000

-150

-140

-130

-120

-110

-100

-90

-80

-70

-60

-50 PTR Phase

Phase (

Deg)

Frequency (Hz)1 10 100 1000

-16

-14

-12

-10

-8

-6

-4

-2

Undisturbed Demin Gel

New Demin Gel Added

LUM phase

Phase (

Deg)

Frequency (Hz)

136

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